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Q.
If the tangent at the point $P$ on the circle $x^2+y^2+6 x+6 y=2$ meets the straight line $5 x-2 y+6=0$ at a point $Q$ on the $y$-axis, then the length of $P Q$ is
Conic Sections
Solution:
The line $5 x-2 y+6=0$ meets the $y$-axis at the point $(0,3)$ and therefore the tangent has to pass through the point $(0,3)$ and required length is therefore,
$ =\sqrt{x_1^2+y_1^2+6 x_1+6 y_1-2}$
$ =\sqrt{0+3^2+6(0)+6(3)-2}$
$ =\sqrt{25}=5$