Exercise [Ellipse, Parabola, Hyperbola]

EXERCISE

Ellipse

1) Draw an ellipse when the distance of its vertex from its directrix is 30 mm and distance of its focus from directrix is 50 mm

2) The Focus of an ellipse is 55 mm away from its directrix. The eccentricity is 5/8. Draw the curve and measure major and minor axes. Also draw tangent and normal through any point located on the curve.

3) Construct a conic when the distance of its focus from its directrix is equal to 40 mm and its eccentricity is 3/4. Name the curve. Draw a tangent and normal at a joint P, 60 mm away from 4 the directrix.

4) The major and minor axes of an ellipse are 120mm and 100mm long respectively. Construct the curve by Rectangular method.

5) Construct an ellipse of major axis 90mm and minor axis 70mm by concentric circles method.

6) Construct an ellipse by parallelogram method taking the major and minor axes as 100mm and 80mm long respectively and the angle between them as 80°.

7) Construct an ellipse by arcs of circles method, major axis being 80mm and the distance between the foci is 60mm.

Parabola

1) Construct a conic when the distance between its focus and directrix is equal to 40 mm and its eccentricity is one. Name the curve.

2) Draw the locus of a point which moves in such a manner that its distance from a fixed point is equal to its distance from a fixed straight line. Take the distance between the fixed point and the fixed line is 70 mm. Name the curve.

3) Construct a parabola whose focus is at a distance of 35 mm from the directrix. Measure the double ordinate through a point at 80 mm distance from directrix. Also draw a tangent and a normal to the curve through a point P, located at a distance 80 mm from the directrix.

4) A cricket ball is thrown from the ground level, reaches to a maximum height of 6m above the ground level and travel a horizontal distance of 14m from the point of projection. Trace the path of ball.

5) Construct a parabola by parallelogram method, base and axis being 140mm and 80mm respectively and the angle between base and axis being 85°.

6) Construct a parabola by offset method, base and axis being 150mm and 75mm long respectively. 

Hyperbola

1) Construct a conic when the eccentricity is 5/4 and the distance between directrix and the focus entris 60 mm. Name the curve.

2) The Focus of a hyperbola is 50 mm from its directrix. Draw the curve when eccentricity is 5/3. Draw a tangent and a normal to the curve at any point on the hyperbola.

3) Draw a hyperbola when its vertex and its focus are at a distance of 25 mm and 40 mm respectively from the directrix. Also draw a tangent and a normal to the hyperbola through a point 75 mm from directrix.