Consider the parameters and of a hyperbola whose centre is the origin and whose…

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider the parameters

a, b

and

c

of a hyperbola whose centre is the origin and whose transverse axis lies along the

x

-axis. (i) State the relation connecting

a, b

and

c

. (ii) The eccentricity

e

of the hyperbola is defined as

e=c/a

. Explain clearly why

e

must always be greater than

1

. (iii) For a hyperbola with

a=4

and

b=3

, calculate its eccentricity and verify that your answer is consistent with the conclusion obtained in part (ii).