AP EAPCET 23-Aug-2021 Shift 2 Paper

Given, in a hyperbola, the length of transverse axis is twice that of the conjugate axis.
The equation of standard hyperbola is

x2

a2

−

y2

b2

=1
∵ Length of transverse axis =2× length of conjugate axis
2a=2×2b
⇒a=2b
∵b2=a2(e2−1)
⇒

a2

4

=a2(e2−1)
⇒e2=1+

1

4

=

5

4

⇒e=

√5

2

∴ Distance between its directrix =

2a

e

=

2(2b)

√5∕2

=

8b

√5