The line $x \cos \alpha+y \sin \alpha=p$ touches the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, if
(A) $a^2 \cos ^2 \alpha-b^2 \sin ^2 \alpha=p^2$
(B) $a^2 \cos ^2 \alpha-b^2 \sin ^2 \alpha=\dot{p}$
(C) $a^2 \cos ^2 \alpha+b^2 \sin ^2 \alpha=p^2 c$
(D) $a^2 \cos ^2 \alpha+b^2 \sin ^2 \alpha=p$