If the angle between the asymptotes of hyperbola \( \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{...

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If the angle between the asymptotes of hyperbola \( \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1 \) is \( 120^{\circ} \) and the product of perpendiculars drawn from the foci upon its any tangent is 9 , then the locus of the point of intersection of perpendicular tangents of the hyperbola can be:
(a) \( x^{2}+y^{2}=6 \)
(b) \( x^{2}+y^{2}=9 \)
(c) \( x^{2}+y^{2}=3 \)
(d) \( x^{2}+y^{2}=18 \)
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