NCERT Class 11 Maths Conic Sections

In the preceding Chapter 10, we have studied various forms of the equations of a line. In this chapter, we shall study 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.

11.2 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 a (Fig11.1). Suppose we rotate the line m around the line l in such a way that the angle a remains constant. Then the surface generated is a double-napped right circular hollow cone hereinafter referred as

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