ncert books for class maths cbsc

transformed. – BERTRAND RUSSELL v . Introduction In the preceding Chapter , we have studied various forms of the equations of a line. In this Chapter, we shall study about some other curves, viz., circles, ellipses, parabolas and hyperbolas.

The names parabola and hyperbola are given by Apollonius. These curves are in fact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with a double napped right circular cone. These curves have a very wide range of applications in fields such as planetary motion, design of telescopes and antennas, reflectors in flashlights and automobile headlights, etc. Now, in the subsequent sections we will see how the intersection of a plane with a double napped right circular cone results in different types of curves.

. Sections of a Cone Let l be a fixed vertical line and m be another line intersecting it at a fixed point V and inclined to it at an angle α (Fig11. ). Suppose we rotate the line m around the line l in such a way that the angle α remains constant.

Then the surface generated is a double-napped right circular hollow cone herein after referred as Apollonius ( B.C. - B.C.)