For the hyperbola

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

For the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

, the normal at point

P

meets the transverse axis

AA'

G

and the conjugate axis

BB'

g

, and

CF

is perpendicular to the normal from the centre. Find the eccentricity of the hyperbola that is the locus of the midpoint of

G

and

g

. (1)

\frac{1}{\sqrt{(e^2 - 1)}}

(2)

\frac{e}{\sqrt{(e^2 - 1)}}

(3)

2\sqrt{(e^2 - 1)}

(4)

\frac{e}{2}