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  4. If the tangent at point P on the circle x2+y2+6 x+6 y-2=0 meets the straight line 5 x-2 y+6=0 at a point Q on the y-axis, then length P Q is

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Q. If the tangent at point $P$ on the circle $x^{2}+y^{2}+6 x+6 y-2=0$ meets the straight line $5 x-2 y+6=0$ at a point $Q$ on the $y$-axis, then length $P Q$ is

Bihar CECEBihar CECE 2009

Solution:

$x^{2}+y^{2}+6 x+6 y-2 =0$
Centre $(-3-3)$ radius $=\sqrt{9+9+2}$
$=\sqrt{20}$
image
Now, $Q C=\sqrt{(-3)^{2}+6^{2}}=\sqrt{45}$
In right $\Delta C P Q$
$P Q=\sqrt{45-20}=5$