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If $P(\theta)$ lies on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ and $S$ and $S^{\prime}$ are foci of the hyperbola,
then $S P . S^{\prime} P=$

MathematicsHyperbolaMHT CETMHT CET 2020 (14 Oct Shift 2)

Options:

A $a^{2} \tan ^{2} \theta-b^{2} \sec ^{2} \theta$
B $a^{2} \tan ^{2} \theta+b^{2} \sec ^{2} \theta$
C $a^{2} \sec ^{2} \theta+b^{2} \tan ^{2} \theta$
D $a^{2} \sec ^{2} \theta-b^{2} \tan ^{2} \theta$

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