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10-1.Circle and System of Circles
medium
The line $x\cos \alpha + y\sin \alpha = p$will be a tangent to the circle ${x^2} + {y^2} - 2ax\cos \alpha - 2ay\sin \alpha = 0$, if $p = $
A
$0$ or $a$
B
$0$
C
$2a$
D
$0$ or $2a$
Solution
(d) $x\cos \alpha + y\sin \alpha – p = 0$ 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 $a$.
$\left| {\frac{{a{{\cos }^2}\alpha + a{{\sin }^2}\alpha – p}}{{\sqrt 1 }}} \right| = a$
$i.e.$ $|a – p|\; = a \Rightarrow p = 0$ or $p = 2a$.
Standard 11
Mathematics