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The product of the perpendiculars from the foci on any tangent to the hyperbola $\frac{x^{2}}{64} - \frac{y^{2}}{9} = 1$ is

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Correct option is B

Equation of a tangent at (8sec⁡ θ, 3tan⁡ θ) the hyperbola is x8sec⁡ θ−y3tan⁡ θ=1If e is the eccentricity of the hyperbola; product of the perpendiculars=(esec⁡θ−1)(−esec⁡θ−1)sec2⁡θ64+tan2⁡θ9=1−e2sec2⁡θ×(64×9)9sec2⁡θ+64tan2⁡θ=1−64−964sec2⁡θ(64×9)9sec2⁡θ+64tan2⁡θ=64tan2⁡θ+9sec2⁡θ9sec2⁡θ+64tan2⁡θ×9=9.

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Statement-1: The locus of the point of intersection of the tangents that are at right angles to the hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{16} = 1 is the circle x^{2} + y^{2} = 52$

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