A) \[3\pi /4\]
B) \[\pi /2\]
C) \[3\pi /2\]
D) \[\pi /6\]
Correct Answer: B
Solution :
Let directrix be x = ale and the focus be S (ae, 0). Let P(a sec \[\text{ }\!\!\theta\!\!\text{ }\], b tan \[\text{ }\!\!\theta\!\!\text{ }\]) be any point on the curve. Equation of tangent at P is \[\frac{\text{x}\,\text{sec}\,\text{ }\!\!\theta\!\!\text{ }}{a}-\frac{y\,\tan \,\text{ }\!\!\theta\!\!\text{ }}{b}=1\] Let F be the intersection point of the tangent and the directrix, so that \[F\equiv \left( \frac{a}{e},\frac{b(\sec \theta -e)}{e\tan \theta } \right)\] \[\Rightarrow \] \[{{m}_{SF}}=\frac{b(\sec \theta -e)}{-a\,\tan \theta ({{e}^{2}}-1)},\] \[{{m}_{PS}}=\frac{b\tan \theta }{a(\sec \theta -e)}\] \[\Rightarrow \] \[{{m}_{SF}}.{{m}_{ps}}=-1\] \[\theta =\frac{\pi }{2}\]You need to login to perform this action.
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