The line $x \cos \alpha + y \sin \alpha =p$ is a tangent to the ellipse. $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ if

Question

$\begin{array}{1 1}(A)\;a^2 \cos ^2 \alpha -b^2 \sin ^2 \alpha =p^2 \\(B)\;a^2 \sin ^2 \alpha -b^2 \cos^2 \alpha =p^2 \\(C)\;a^2 \cos^2 \alpha + b^2 \sin ^2 \alpha =p^2 \\(D)\;a^2 \cos^2 \alpha+b^2 \sin ^2 \alpha=p \end{array}$