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

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If the angle between the asymptotes of hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} \)
\( \mathrm{P} \) \( =1 \) is \( 120^{\circ} \) and the product of perpendiculars drawn from

W the foci upon its any tangent is 9 , then the locus of the point of intersection of perpendicular tangents of the hyperbola can be
(1) \( x^{2}+y^{2}=6 \)
(2) \( x^{2}+y^{2}=9 \)
(3) \( x^{2}+y^{2}=3 \)
(4) \( x^{2}+y^{2}=18 \)
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