If the line $x \cos \alpha + y \sin \alpha = p$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then:
- A$a^2 \cos^2 \alpha - b^2 \sin^2 \alpha = p^2$
- B$a^2 \cos^2 \alpha + b^2 \sin^2 \alpha = p^2$
- C$a^2 \sin^2 \alpha - b^2 \cos^2 \alpha = p^2$
- D$a^2 \sin^2 \alpha + b^2 \cos^2 \alpha = p^2$
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