If the straight line $x\cos \alpha + y\sin \alpha = p$ be a tangent to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, then
If the straight line $x\cos \alpha + y\sin \alpha = p$ be 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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