Question

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

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

Answer 1

The correct option is C $5$ units

$5x-2y+6=0$
$y$-intercept of the line is $Q(0,3).$
So tangent at $P$ on $x^2+y^2+6x+6y-2=0$ passes through $Q(0,3)$ as per the given condition.

$\therefore PQ=$ length of tangent to circle from $(0,3)$
$=\sqrt{S_1}=5$ units