question_answer

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

A) 4

B) \[2\sqrt{5}\]              

C) 5

D) \[3\sqrt{5}\]

Correct Answer: C

Solution :

At point \[{{Q}_{1}}\,\,\,x=0\]

\[\therefore \]in line \[5x-2y+6=0\]

Put       \[x=0\]  \[\Rightarrow \]   \[y=3\]

\[\therefore Q(0,3)\]

\[\therefore PQ=\sqrt{{{0}^{2}}+{{3}^{2}}+6(0)+6(3)-2}=5\]