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
• C. 5
• D. 4

Answer 1

The correct option is C

5

The line 5x - 2 y + 6 = 0 cuts y axis at Q (0 , 3) . Clearly PQ is the lenght 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