NCERT Book Class 11 Maths Chapter 10 Conic Sections

176 MATHEMATICS

Chapter 10
CONIC SECTIONS

vLet the relation of knowledge to real life be very visible to your pupils
and let them understand how by knowledge the world could be
transformed. – BERTRAND RUSSELL v

10.1 Introduction
In the preceding Chapter 10, 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, Apollonius
design of telescopes and antennas, reflectors in flashlights (262 B.C. -190 B.C.)

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.

10.2 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 α (Fig10.1).
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 Fig 10. 1