If the normal to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) at any point \( P...

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If the normal to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) at any point \( P \) \( (a \sec \theta, b \tan \theta) \) meets the transverse and conjugate axes in \( G \) and \( g \) respectively and if \( f \) is the foot of perpendicular to the normal at \( P \) from the centre \( C \) , then minimum of \( P G \) is
(a) \( \frac{b^{2}}{a} \)
(b) \( \left|\frac{a}{b}(a+b)\right| \)
(c) \( \left|\frac{b}{a}(a-b)\right| \)
(d) \( \left|\frac{a}{b}(a-b)\right| \)
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