Mathematics

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. a. (i) State the relation connecting

a, b

and

c

. b. (ii) The eccentricity

e

of the hyperbola is defined as

e=c/a

. Explain clearly why

e

must always be greater than

1

. c. (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).