If the tangent at the point \( (a \sec \alpha, b \tan \alpha) \) to the hyperbola \( \frac{x^{2}...

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If the tangent at the point \( (a \sec \alpha, b \tan \alpha) \) to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \)
meets the transverse axis at \( \mathrm{T} \), then distence of \( \mathrm{T} \) form focus of hyperbola is
(a) \( a(e \pm \cos \alpha) \)
(b) ae
(c) \( b(e-\cos \alpha) \)
(d) \( \sqrt{a^{2} e^{2}+b^{2} \cot ^{2} \alpha} \)
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