Question

From a point $P(2,2\sqrt{2})$ tangents $PO$ and $PR$, are drawn to the circle $x^2+y^2=a^2$. If $OR$ is touching the circle $x^2+y^2=3$, then value of '$a$'

• A. $4$
• B. $2\sqrt{3}$
• C. $3\sqrt{2}$
• D. $\sqrt{6}$

Answer 1

The correct option is D $\sqrt{6}$

$e{q}^n$ of chord of contact from $p(2,2\sqrt{2})$ to $x^2+y^2=a^{2}is$
$T=0\Rightarrow 2x+2\sqrt{2}y=a^2$---{1}
$LineR:2x+2\sqrt{2}y=a^2$
then, line oR is also a tongent for $x^2+y^2=3$ is
then $r=\sqrt{3}=|\frac{0+0-a^2}{\sqrt{4+8}}|$
$2\times 3=|a^2|$
$\Rightarrow a=\pm \sqrt{6}$