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The line $x \cos \alpha+y \sin \alpha=p$ will be a tangent to the circle $x^2+y^2-2 a x \cos \alpha-2 a y \sin \alpha=0$, if $p=$
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$0$ or $2 a$
$x \cos \alpha+y \sin \alpha-p=0$ is a tangent, if perpendicular from centre on it is equal to radius of the circle. Here centre is $(a \cos \alpha, a \sin \alpha)$ and radius is $a$.
$\therefore\left|\frac{a \cos ^2 \alpha+a \sin ^2 \alpha-p}{\sqrt{1}}\right|=a$
i.e. $|a-p|=a \Rightarrow p=0$ or $p=2 a$
$\therefore\left|\frac{a \cos ^2 \alpha+a \sin ^2 \alpha-p}{\sqrt{1}}\right|=a$
i.e. $|a-p|=a \Rightarrow p=0$ or $p=2 a$
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