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
  $a^2 \sin^2 \alpha + b^2 \cos^2 \alpha = p^2$