At the point of intersection of the rectangular hyperbola \( x y=c^{2} \) and the parabola \( y^...

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At the point of intersection of the rectangular hyperbola \( x y=c^{2} \) and the parabola \( y^{2}=4 \mathrm{ax} \) tangents to the rectangular hyperbola and the parabola make an angle \( \theta \) and \( \phi \) respectively with the axis of \( X \), then-
(a) \( \theta=\tan ^{-1}(-2 \tan \phi) \)
(b) \( \phi=\tan ^{-1}(-2 \tan \theta) \)
(c) \( \theta=\frac{1}{2} \tan ^{-1}(-\tan \phi) \)
(d) \( \theta=\frac{1}{2} \tan ^{-1}(\tan \phi) \)
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