Question

If the tangent at the point $P$ on the circle $x^2+y^2+6x+6y=2$ meets the line $5x-2y+6=0$ at a point $Q$ on the $y-$axis, then the length of $PQ=$-______

• A. $4$
• B. $2\sqrt{5}$
• C. $5$
• D. $3\sqrt{5}$

Answer 1

Answer: (C)

$5$

The line $5x-2y+6=0$ meets y-axis at $(0,3)$.
So the
coordinates of $Q$ are$(0,3)$ and $PQ$ is the length of the
tangent from
$Q(0,3)$ to the circle $x^2+y^2+6x+6y-2=0$.
Hence $PQ=\sqrt{0+3^2+6\times 0+6\times 3-2}=\sqrt{25}=5$