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

Equation of circle  is ${\mathrm{x}}^2+{\mathrm{y}}^2+6\mathrm{x}+6\mathrm{y}=2$

Equation of ine $5\mathrm{x}-2\mathrm{y}+6=0$

Tangent intersects y-axis at Q

Q=(0,3)

PQ=Length of tangent from (0,3) is

$\begin{array}{r}PQ=\sqrt{f(0,3)}\\ =\sqrt{0^2+3^2+6.0+6.3-2}\\ =\sqrt{25}\\ =5\end{array}$