\( \mathrm{P} \) For the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{...

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\( \mathrm{P} \)
For the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \), the normal at point \( P \) meets
W the transverse axis \( A A^{\prime} \) in \( G \) and the conjugate axis \( B B^{\prime} \) in \( g \) and \( C F \) be perpendicular to the normal from the centre.
Locus of middle-point of \( G \) and \( g \) is a hyperbola of eccentricity
(1) \( \frac{1}{\sqrt{\left(e^{2}-1\right)}} \)
(2) \( \frac{e}{\sqrt{\left(e^{2}-1\right)}} \)
(3) \( 2 \sqrt{\left(e^{2}-1\right)} \)
(4) \( \frac{e}{2} \)
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