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The condition that the line \( p=x \cos \alpha+y \sin \alpha \) becomes a tangent to \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) is
\( \mathrm{P} \)
(A) \( \mathrm{p}=\mathrm{a} \cos \alpha-\mathrm{b} \sin \alpha \)
(B) \( \mathrm{p}^{2}=\mathrm{a}^{2} \cos \alpha-\mathrm{b}^{2} \sin \alpha \)
(C) \( \mathrm{p}^{2}=\mathrm{a}^{2} \cos ^{2} \alpha+\mathrm{b}^{2} \sin ^{2} \alpha \) (D) \( \mathrm{p}^{2}=\mathrm{a}^{2} \cos ^{2} \alpha-\mathrm{b}^{2} \sin ^{2} \alpha \)
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