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UNIT I

CONIC CURVES

1. Draw an ellipse given the following distance of the focus from the directrix=60mm.Eccentricity=3/4. Draw the tangent & normal at any point on the curve.

2. Draw a parabola when the distance of the focus from the directrix is equal to 40mm.Also, draw the tangent normal lines at any point on the curve.

3. Construct a cycloid given the radius of the generating circle is 30mm. Draw thetangent & normal at a distance of 100mm from the center of the circle on the curve.

4. A circular disc of radius 25mm rolls on a plane surface without slipping. Trace a pointP on the circumference on the circle for one complete revolution. Draw the tangent &

normal at any point on the curve.

5. Construct the hyperbola when the distance from focus to the (i) directrix=60mm, (ii)eccentricity=3/2. Draw the tangent & normal at any point on the curve.

6. Draw a parabola the distance of focus from directrix =40mm. Draw the tangent &normal at any point on the curve.

7. Draw the locus of a curve traced by a point when the distance of focus from thedirectrix= 35mm and eccentricity is 4/3. Also, draw the tangent normal lines at any point on

the curve.

8. An inelastic string of 150mm length has one of its ends attached to thecircumference of a circular disc of 40mm diameter. Draw the cure traced by the other end

of the string when it is completely unwound around the disc keeping the string always tight.

Also, draw the tangent & normal to the obtained curve at a point 100mm away from the

center of the disc.

9. Draw the locus of a point P moving so that the ratio of the distance from a fixedpoint F to its distance from a fixed straight line is 1. The point P is at a distance of 30 mm

from the fixed straight line. Also, the draw tangent and normal to the generated curve.

10. Draw the locus of a point which moves in a plane in such a way that the ratio of itsdistances from a fixed point F and a fixed straight line AB is always distance between 2/3.

The distance between the fixed point F and fixed straight line is 50mm. Also, draw a tangent

and normal on a point on the locus at a horizontal distance of 55mm from the fixed straight

line.

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11. Draw the involute of a circle of diameter 50mm when a string is unwound in theclockwise direction. Draw the tangent and normal at a point located on the involute.

12. Draw the locus of a point P moving so that the ratio of the distance from a fixedpoint F to its distance from a fixed straight line is . Point F is at a distance of 35 mm from

the fixed straight line. Also draw the tangent and normal to the curve.

13. A circular wheel of 40mm diameter rolls without slipping along a straight line. Drawthe curve traced by a point P lying on the rim for 1.25 revolution of the wheel. Name the

curve traced. Also draw the tangent and normal at a point P when the wheel has travelled

80mm from its starting position.

14. Draw a circle of 50mm diameter rolls as a horizontal for half of revolution clockwiseand the on a line inclined at 60 to the horizontal for another half clockwise. Draw the curve

traced by a point on the circumference of the circle taking the topmost point of the rolling

circle as the initial position of the generating point.

15. Draw the involute of a square of side 25mm. Also draw the tangent and normal tothe curve.

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