UNIT_II - Projection of Points & Lines

UNIT_II

PROJECTION OF POINTS:

1. Draw the projections of the following points on the same line, keeping the Projectors 20mm apart.

(a) Point C, in V.P. and 40mm above H.P. 

(b) Point D, 25mm below the H.P. and 25mm behind the V.P.

(c) Point E, 15mm above H.P. and 50mm behind V.P.

(d) Point F, 40mm below H.P. and 25mm in front of V.P.

2.   (a) A point A is 2.5 cm above the H.P. and 3 cm in front of the V.P. Draw its Projections.

(b) A point A is 2 cm below the H.P. and 4 cm behind the V.P. Draw its Projections.

3.   (a) A point P is 15mm above the H.P. and 20mm in front of the V.P. Another point Q is 25mm behind the V.P. and 40mm below the H.P. Draw projections of P and Q keeping the distance between their projectors equal to 90mm.Draw straight lines joining i. their top views and ii. their front views.

(b) A point 30mm above XY line is the plan view of two points P and Q. the elevation of P is 45mm above the H.P. while that of the point Q is 35mm below the H.P. Draw the projections of the points and state their position with reference to the principal planes and the quadrant in which they lie.

4.   Two points P and Q are in the H.P. The point P is 30 mm in front of V.P. and Q is behind the V.P. The distance between their projectors is 80 mm and line joining their top views makes an angle of 40⁰ with XY. Find the distance of the point Q from the V.P.

5.   (a) A point A is 20mm above H.P. and in I quadrant. Its shortest distance from the reference line XY is 40mm. Draw the projections of the point and determine its distance from V.P.

(b) A point at 25mm above the reference line XY is the front view of two points A and B. The top view of A is 40mm behind V.P and the top view of B is 50mm in front of V.P. Draw the projections of the points and state their positions relative to the planes of projection and the quadrants in which they lie.

6.   A point P is 20mm below HP and lies in III quadrant. Its shortest distance from xy is 40mm. Draw its projections.

7.  (a) Draw the projections of the following points on the same ground line, keeping the Projectors 25mm apart.     (i). A, in the H.P. and 20 mm behind the V.P.

(ii). B, 40mm above the H.P. and 25mm in front of the V.P.

(b) State the quadrants with the help of drawing, in which the following points are situated

                         i.      A point P; its top view is 40mm above xy; the front view 20 mm below the top view.

                        ii.      A point Q; its projections coincide with each other 40mm below xy.

8.  (a) The point A is on H.P. and 40mm in front of V.P. Another point B is on V.P. and below H.P. The line joining their front views makes an angle of 45⁰ with x y, while the line joining their top views makes an angle of 30⁰. Find the distance of the point B from H.P.

(b) Draw the projections of the following points in III quadrant when the

                 i. Point A lies in the H.P. and 22mm away from V.P. 

                ii. Point B lies in V.P. and 32mm away from H.P.

               iii   Point C lies 32mm from H.P. and 22mm from V.P.

9.  (a) A point P is 15mm above the H.P. and 20mm in front of the V.P. Another point Q is 25mm behind the V.P. and 40mm below the H.P. Draw projections of P and Q keeping the distance between their projectors equal to 90mm. Draw straight lines joining i. their top views and ii. their front views.

(b) A point 30mm above xy line is the plan view of two points P and Q. the elevation of P is 45mm above the H.P. while that of the point Q is 35mm below the H.P. Draw the projections of the points and state their position with reference to the principal planes and the quadrant in which they lie.

10. (a) Two points A and B are on H.P; the point  A being 30mm in front of V.P., while B is 45mm behind V.P. The line joining their top views makes an angle of 45⁰ with xy. Find the horizontal distance between two points.

(b) Find the distance between two points A and B when B is 40mm in front of V.P. and 25mm above H.P. The point A is 25mm behind the V.P. and 40mm below H.P. The distance between projectors measured along xy line being 40mm.

11.(a) Draw the projectors of the following points in different quadrants.

                  i.      Point A, 25mm in front of V.P., 30mm above H.P

                 ii.      Point B, 22mm behind V.P., 28mm above H.P.

                iii.      Point C, 28mm behind V.P., 30mm below H.P 

                 iv.      Point D, 40mm in front of V.P., 25mm below H.P

(b) A point P is 25mm in front of the V.P. and 40 mm above the H.P. Another point Q is 40mm in front of the V.P. and 25mm above the H.P. The distance measured between the projectors is 40mm. Draw the projections and find the distance between P and Q.

PROJECTION OF LINES:

1. (a) A line CD measures 80mm is inclined at an angle of 30⁰ to HP and 45⁰ to VP. The point C is 20mm above HP and 30mm in front of VP. Draw the projections of the line.

(b) Draw the projections of a line JK 70 mm long and touching both HP and VP. It is inclined at 40⁰ to HP and 35⁰ to VP.

2.  A line AB is 30 mm long and inclined at 30⁰ to VP and parallel to HP. The end A of the line is 15 mm above HP and 20mm in front of VP. Draw the projections.

3.  (a) A line CD is parallel to VP and inclined at 40⁰ to HP. C is in HP and 25 mm in front of VP. The length of the top view is 50mm. Determine its true length.

(b) A line measuring 80 mm long has one of its ends 60mm above HP and 20mm in front of VP. The other end is 15 mm above HP and in front of VP. The front view of the line is 60 mm long. Draw the top view.

4.  (a) A line AB 25mm long is perpendicular to V.P. and parallel to H.P. Its end A is 10mm in front of V.P. and the line is 20mm above H.P. Draw the projections of the line.

(b) A line MN 50mm long is parallel to V.P. and inclined at 30⁰ to H.P. The end M is 20mm above H.P. and 10mm in front of V.P. Draw the projections of the line.

5.  (a) A line AB, 65 mm long has its end A in the H.P. and 15 mm in front of the V.P. The end B is in III quadrant. The line is inclined at 30⁰ to the H.P. and at 60⁰ to the V.P. Draw its projections.

(b) A line PQ 75 mm long has its end P in both HP and VP. It is inclined at an angle of 30⁰ to HP and 45⁰ to VP. Draw projections of the line.

6. The distance between the projectors of two points A and B is 70 mm. Point A is 10 mm above HP and 15 mm in front of VP. Point B is 50 mm above HP and 40 mm in front of VP. Find the shortest distance between A and B. Measure true inclination of the line AB with HP and VP.

7. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP. Draw the projections of the line. Find it inclination with HP.

(b) A line AB 60mm long is parallel to HP. The point P is 20mm above HP and 35 mm in front of VP. The length of the front view is 50mm. Determine its true inclination with VP.

8. (a) The length of the top view of a line MN parallel to VP and inclined at 45⁰ to the HP is 50 mm. Point M is 12 mm above HP and 25 mm in front of VP. Draw the projection of the line. Find the true length.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of front view is 35 mm. Draw the projections of the line. Find its inclination with VP.

9.  A 90 mm long line is parallel to and 25 mm in front of V.P. Its one end is in the H.P. while other end is 50 mm above the H.P. Draw the projections of the line and find its inclination with H.P.

10. The length of the top view of a line is 40mm and the length of the front view is 50mm, the top view is inclined at 30⁰ to xy. Draw the projections of the line, assuming that its one end is situated on H.P. and 25mm in front of V.P. Determine the inclinations of the line with H.P and V.P.

11. (a) Draw the projection of a line CD 50 mm long, parallel to HP and inclined to VP. The end of C is 10 mm in front of VP and D is 30 mm in front of VP. The line is 15 mm above HP.

(b) A line AB is 75 mm long. A is 50 mm in front of VP and 15 mm above HP. B is 15mm in front of VP and is above HP. Top view of AB is 50mm long. Draw and measure the front view. Find the true inclinations.

12. (a) A line PQ, 9cm long, is in the H.P. and makes an angle of 30⁰ with the V.P. Its end P is 2.5cm in front of the V.P. Draw its projections.

(b) The front view of a 7.5cm long line measures 5.5cm. The line is parallel to the H.P. and one of its end is in the V.P. and 2.5cm above the H.P. Draw the projections of the line and determine its inclination with V.P. 

13. Two pegs fixed on a wall are 4.5metres apart. The distance between the pegs measured parallel to the floor is 3.6 meters. If one peg is 1.5 meters above the floor, find the height of the second peg and the inclination of the line joining the two pegs, with the floor.

14. A 100 mm long line is parallel to and 40 mm above the H.P. Its two ends are 25 mm and 50 mm in front of the V.P. respectively. Draw the projections of the line and determine its inclination with the V.P.

15. A line AB, 50mm long, has its end A in both the H.P. and the V.P. Its is inclined at 30⁰ to the H.P and at 45⁰ to the V.P. Draw its projections.

16. (a) The top view of a 75 mm long line measures 55 mm. The line is in the V.P., its one end being 25 mm above H.P. Draw its projections.

 (b) The front view of a line, inclined at 3⁰⁰ to the V.P. is 65 mm long. Draw the projection of the line, when it is parallel to and 40 mm above the V.P., its one end being 30mm in front of the V.P.

17. Draw the projections of a 75 mm long straight line, in the following positions:

a.        Parallel to both the H.P. and the V.P. and 25 mm from each.

b.       parallel to 30 mm above H.P. and in the V.P.

c.        parallel to 40 mm in front of V.P. and in the H.P

18. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP. Draw the projections of the line. Find its inclination with HP.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of the front view is 35 mm. Draw the projections of the line. Determine its inclination with VP.

19. A room measures 8m long, 5m wide and 4m high. An electric bulb hangs in the centre of the ceiling and 1m below it. A thin straight wire connects the bulb to a switch kept in one of corner of the room and 1.25m above the floor. Draw the projections of the wire, also determine its true length and slope with the floor.

20. A line AB, 90 mm long, is inclined at 45⁰ to the HP and its top view makes an angle of 60⁰ with the VP. The end A is in the HP and 12 mm in front of the VP. Draw its front view and find its true inclination with the VP.

21. (a) A line AB is 75 mm long. A is 50 mm in front of VP and 15 mm above HP. B is 15 mm in front of VP and is above HP. Top View of AB is 50mm long. Draw and measure the front view. Find the true inclinations.

(b) A line measuring 80 mm long has one of its ends 60 mm above HP and 20 mm in front of VP. The other end is 15 mm above HP and in front of VP. The front view of the line is 60 mm long. Draw the top view.

22. (a) A line AB 40 mm long is parallel to VP and inclined at 35⁰ to HP. The end A is 15 mm above HP and 20 mm in front of VP. Draw the projections of the line and find its traces.

(b) A line MN 50 mm long is parallel to VP and inclined at 45⁰ to HP. The end M is 20 mm above HP and 15 mm in front of VP. Draw the projections of the line and finds its traces.

23. (a) The line EF 60 mm long is in VP and inclined to HP. The top view measures 45 mm. The end E is 15 mm above HP, Draw the projections of the line. Find its inclination with HP.

(b) A line GH 45 mm long is in HP and inclined to VP. The end G is 15 mm in front of VP. The length of the front view is 35 mm. Draw the projections of the line. Determine its inclination with VP.

24. A line AB of 70mm long, has its end A at 10mm above H.P. and 15mm in front of V.P. Its front view and top view measure 50mm and 60mm respectively. Draw the projections of the line and determine its inclinations with H.P. and V.P.

25. A line AB, 80 mm long, makes an angle of 30⁰ with the V.P. and lies in a plane perpendicular to both the H.P. and the V.P. Its end A is in the H.P. and the end B is in the V.P. Draw its projections.

26. A 95 mm long line is parallel to and 50 mm above the H.P. Its two ends are 20 mm and 50 mm in front of the V.P. respectively. Draw its projections and find its inclination with the V.P.

27. A line PQ, 100mm long, is inclined at 45⁰ to the H.P. and at 30⁰ to the V.P. Its end P is in II quadrant and Q is in IV quadrant. A point R on PQ, 40mm from P is in both the planes. Draw the projections of PQ.

28. A line of 75mm long has one of its ends 50mm in front of V.P. and 15mm above H.P. The top view of the line is 50mm long. Draw and measure the front view. The other end is 15mm in front of V.P. and is above H.P.

29. A line CD 80mm long is inclined at an angle of 30⁰ to H.P. and 45⁰ to V.P. The point C is 20mm above H.P. and 30mm in front of V.P. Draw the projections of the straight line.

30. (a) A line CD 30 mm long is perpendicular to V.P. and parallel to H.P. Its end C is 5mm in front of V.P. and the line is 10mm above H.P. Draw the projections of the line.

(b) A line PQ 40mm long is parallel to V.P. and inclined at an angle of 30⁰ to H.P. The end P is 15mm above H.P. and 20mm in front of V.P. Draw the projections of the line.

31. The projectors of the ends of a line AB are 5cm apart. The end A is 2cm above the H.P. and 3cm in front of the V.P. The end B is 1cm below the H.P. and 4cm behind the V.P. Draw the projections of AB and determine its inclinations with the H.P. and the V.P.

32. (a) A line PQ 75mm long has its end P in the V.P and the end Q in the H.P. The line is inclined at 30⁰ to the H.P. and at 60⁰ to the V.P. Draw its projections.

(b) Draw the projections of a 65mm long straight line, in the following positions:

a.        Parallel to both the H.P and the V.P and 25mm from each.

b.       Perpendicular to the H.P in the V.P and its one end in the H.P.

33. The top view of a line AB, 75mm long measures 50mm. The end A is 40mm in front of VP and 15mm below H.P. B is 15mm in front of V.P. and is above H.P. Draw the projections of the line and determine the distance of B from H.P. and also the inclinations of the line AB with both the planes.

34. A line AB, 65mm long, has its end A 20mm above the H.P. and 25mm in front of the V.P. The end B is 40mm above the H.P. and 65mm in front of the V.P. Draw the projections of AB and show its inclinations with the H.P. and the V.P. 

35. The top view of a 75mm long line AB measures 65mm, while the length of its front view is 50mm. Its one end A is in the H.P. and 12mm in front of the V.P. Draw the projections of AB and determine its inclinations with the H.P. and the V.P.

36. (a) The top view of a 75mm long line measures 55mm. The line is in the V.P., its one end being 25mm above the H.P. Draw its projections.

(b) Draw the projections of a 75mm long line, in the following positions:

a.        Parallel to and 30mm above the H.P and in the V.P.

b.       Inclined at 30⁰ to the H.P and its one end 20mm above the H.P, parallel to and 25mm in front of the V.P.

37. A line AB, 65mm long, has its end A 20mm above the H.P. and 25mm in front of the V.P. The end B is 40mm above the H.P. and 65mm in front of the V.P. Draw the projections of AB and show its inclinations with the H.P. and the V.P.

Mid Point Problems:

38.A line AB 120 mm long is inclined at 45⁰ to HP and 30⁰ to the VP. Its midpoint C is in VP and 20 mm above HP. The end A is in III quadrant and B is in I quadrant. Draw the projections of the line.

39.Draw the projections of a line AB, 90mm long, its midpoint M being 50mm above the H.P. and 40mm in front of V.P. The end A is 20mm above H.P. and 10mm in front of V.P. Show the inclinations of the line with H.P. and V.P.

40. The midpoint of a straight line AB is 60mm above H.P. and 50mm in front of V.P. The line measures 80mm long and inclined at 30⁰ to H.P. and 45⁰ to V.P. Draw its projections.

41. A line of 100mm long makes an angle of 35⁰ with H.P. and 45⁰ with V.P. Its midpoint is 20mm above H.P. and 15mm in front of V.P. Draw the projections of the line.

42. The front view of a 125 mm long line PQ measures 80 mm and its top view measures 100 mm. Its end Q and the midpoint M are in I quadrant, M being 20 mm from both the planes. Draw the projections of the line PQ.

UNIT_I - Engineering Curves

UNIT_I

1. (a) Construct a rectangular hyperbola when a point P on it is at a distance of 18 mm and 34 mm from two asymptotes. Also draw a tangent to the curve at a point 20 mm from an asymptote.

(b) The vertex of a hyperbola is 60 from its focus. Draw the curve, if the eccentricity is 3/2. Draw a normal and a tangent at a point on the curve, 75 from the directrix.

2. (a) The major axis of an ellipse is 100 mm long and the distance between its foci is 70 mm. Draw the ellipse.

(b) Draw a hyperbola having the double ordinate of 100 mm, the abscissa of 60 mm and the transverse axis of 100 mm.

3. (a) Construct a pentagon length of a side is 30 mm.

(b) Draw an arc passing through three points not in straight line.

(c) Construct a parabola, with the distance of the focus from the directrix as 50 mm, also draw normal and tangent to the curve at a point 40 from the directrix.

4. (a) Inscribe a regular octagon in a given square of 50 mm side.

(b) Construct a parabola with base 60 and length of the axis 40. Draw a tangent to the curve at point 20 from the base. Also locate the focus and directrix to the parabola.

5. A fixed point is 75 mm from a fixed straight line. Draw the locus of a point P moving such a way that its distance from the fixed straight line is (i) twice its distance from the fixed point (ii)equal to its distance from the fixed point. Name the curves.

6. (a) Two points A&B are 100 mm apart. A point C is 75mm from A and 60mm from B. Draw the ellipse passing through A,B and C.

(b) A ball thrown up in the air reaches maximum height of 45 m and travels a horizontal distance of 75m. Trace the path of the ball, assuming it to be parabolic.

7. (a) Inscribe an ellipse in a parallelogram having sides 150 mm and 100 mm long and an included angle of 120⁰.

(b) A point P is 30 mm and 50 mm respectively from two straight lines which are at right angles to each other. Draw the rectangular hyperbola from P within 10 mm distance from each line.

8. (a) A parallelogram has sides 100 &80 mm at an included angle of 700. Inscribe an ellipse in the parallelogram. Find the major and minor axis of the curve.

(b) Draw an ellipse by concentric circles method and find the length of the minor axis with the help of the following data: (i) major axis 100 mm. (ii) distance between foci 80 mm.

9. (a) The major and minor axis of an ellipse is 120&80 mm. Draw an ellipse by arcs of circles method.

(b) The asymptotes of a hyperbola are inclined at 70⁰ to each other. Construct the curve when a point p on it is at a distance of 20 mm and 30 mm from the two asymptotes.

10. Two fixed points A&B are 100 mm apart. Trace the complete path of a point P moving (in the same plane as that of A&B) in such a way that, the sum of its distances from A&B is always the same and equal to 125 mm. Name the curve. Draw another curve parallel to and 25 mm away from this curve.

11. The foci of an ellipse are 90 mm apart and the minor axis is 65 mm long. Determine the length of the major axis and draw half the ellipse by concentric-circles method and other half by oblong method.

12. A circle of 60 mm diameter rolls without slipping on the outside of another circle of diameter 150 mm. Show the path of a point on the periphery of the (generating) rolling circle, diametrically opposite to the initial point of contact between the circle.

13. A circle of 60 mm diameter rolls on a horizontal line for a half revolution and then on a vertical line for another half revolution. Draw the curve traced out by a point p on the circumference of the circle.

14. Draw one turn of the involutes of a hexagon whose inscribed circle is 30mm in diameters.

15. Draw a straight line AB of any length. Make a point F, 65mm from AB .Trace the paths of a point P moving in such a way that the ratio of its distance from the point F, to its distance from AB is (a) 1(b) 2:3 Name each curve. Draw a normal and a tangent to each curve at a point on it 45 mm from F.

16. A fixed point is 75mm from a fixed straight line. Draw the locus of a point P moving such a way that its distance from the fixed straight line is equal to its distance from the fixed point. Name the curve. Draw a normal and tangent on the curve.

17. A fixed point F is 7.5 cm from a fixed straight line. Draw the locus of a point P moving in such a way that its distance from the fixed straight line is 2/3 times its distance from F. Name the curve. Draw normal and tangent at a point 6 cm from F.

18. Two fixed points A and B are 100 mm apart. Trace the complete path of a point P moving (in the same plane as that of A and B) in such a way that the sum of its distances from A and B is always equal to 125 mm. Name the curve. Draw another curve parallel to and 25 mm away from this curve.

19. The major axis of an ellipse is 150mm long and the minor axis is 100mm long. Find the foci and draw an ellipse by ‘arcs of circles’ method. Draw a tangent to the ellipse at a point on it 25mm above the major axis.

20. The vertex of a hyperbola is 65mm from its focus. Draw the curve if the eccentricity is 3/2. Draw a normal and a tangent at a point on the curve, 75 mm from the directrix.

21. Show by means of a drawing that when the diameter of the directing circle is twice that of the generating circle, the hypocycloid is a straight line. Take the diameter of the generating circle equal to 50mm.

22. The foci of an ellipse are 80mm apart and the minor axis is 55mm long. Determine the length of the major axis and draw the ellipse by concentric-circle method. Draw a curve parallel to the ellipse and 20mm away from it.

23. A circle of 50mm diameter rolls on the circumference of another circle of 175mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle for one complete revolution. Name the curve. Draw a tangent and a normal to the curve at a point 125mm from the center of the directing circle.

24. Two straight lines OA and OB make an angle of 75⁰ between them. P is a point 40mm from OA and 50mm from OB. Draw a hyperbola through P, with OA and OB as asymptotes, marking at least ten points.

25. A circle of 35mm diameter rolls on a horizontal line. Draw the curve traced out by a point R on the circumference for one half revolution of the circle. For the remaining half revolution, the circle rolls on the vertical line. The point R vertically above the center of the circle in the starting position.

26. (a) Inscribe an ellipse in a parallelogram having sides 150mm and 100mm long and an inclined angle of 120⁰.

(b) Draw a rectangle having its sides 125mm and 75mm long. Inscribe two parabolas in it with their axis bisecting each other.

27. Draw a hypo cycloid of a circle of 30mm diameter which rolls inside another circle of 160mm diameter, for one revolution counter clock wise. Draw a tangent and a normal to it at a point 60mm from the center of the directing circle.

28. Two points A and B are 50 mm apart. Draw the curve traced out by a point P moving in such a way that the difference between its distances from A and B is always constant and equal to 20 mm.

29. Show by means of a drawing that when the diameter of the directing circle is twice that of the generating circle, the hypocycloid is a straight line. Take diameter of generating circle equal to 60 mm.

30. The major axis of an ellipse is 150 mm long and the minor axis is 100 mm long. Find the foci and draw the ellipse by ‘arcs of circles’ method. Draw a tangent to the ellipse at a point on it 25 mm above the major axis.

31. A point P is 30 mm and 50 mm respectively from two straight lines which are at right angles to each other. Draw a rectangular hyperbola from P within 10 mm distance from each line.

32. A fixed point is 75mm from a fixed straight line. Draw the locus of a point P moving such a way that its distance from the fixed straight line is (a) twice its distance from the fixed point (b) equal to its distance from the fixed point. Name the curves.

33. A circle of 40mm diameter rolls on a straight line without slipping. In the initial position the diameter PQ of the circle is parallel to the line on which it rolls. Draw the locus of the points P and Q for one complete revolution of the circle.

34. Draw a rectangle having its sides 125mm and 75mm long. Inscribe two parabolas in it with their axis bisecting each other.

35. The foci of an ellipse are 90mm apart and the minor axis is 65mm long. Determine the length of the major axis and draw half of the ellipse by concentric circle method and other half by oblong method. Draw a curve parallel to the ellipse and 25mm away from it.

36. Draw a hypocycloid of a circle of 45mm diameter which rolls inside another circle of 200 mm diameter for one revolution. Draw a tangent and normal at any point on it.

37. A circle of 115 mm diameter rolls on another circle of 75mm diameter with internal contact. Draw the locus of a point on the circumference of rolling circle for its one complete revolution.

38. Draw a hypocycloid of a circle of 45mm diameter which rolls inside another circle of 200 mm diameter for one revolution. Draw a tangent and normal at any point on it.

39. A coin of 40mm diameter rolls over horizontal table without slipping. A point on the circumference of the coin is in contact with the table surface in the beginning and after one complete revolution. Draw and name the curve. Draw a tangent and normal at any point on the curve.

40. A circle of 50mm diameter rolls along a straight line without slipping. Draw the curve traced out by a point P on the circumference for 1.5 revolution of the circle. Name the curve. Draw a tangent and normal at a point on it 35mm from the line.

41. (a) A fountain jet discharges water from ground level at an inclination of 50⁰ to the ground. The jet travels a horizontal distance of 9 m from the point of discharge and falls on the ground. Trace the path of the jet.

(b) The distance between two fixed points is 90mm. A point P moves such that the difference of its distance from the two fixed points is always equal to 60mm.Draw the loci of P.

42. Two fixed points A and B are 100mm apart. Trace the complete path of a point P moving (in the same plane as that of A and B) in such a way that, the sum of its distances from A and B is always the same and equal to 125 mm. Name the curve. Draw another curve parallel to and 25mm away from this curve.

43. A circle of 50mm diameter, rolls on a horizontal line for half a revolution clock wise and then on a line inclined at 60⁰ to the horizontal for another half clockwise. Draw the curve traced by a point P on the circumference of the circle, taking the top most point on the rolling circle as the initial position of the generating point.