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 length of PQ = ___

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

Answer 1

The correct option is C 5

The line 5x – 2y + 6 = 0 cuts y-axis at Q(0, 3). Clearly PQ is the length of the tangent drawn from Q on the circle
$x^2+y^2+6x+6y=2\Rightarrow PQ=\sqrt{0+9+6\times 0+6\times 3-2}=5$