question_answer

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

A)  4                            

B)         \[2\sqrt{5}\]     

C)         5                            

D)         \[3\sqrt{5}\]

Correct Answer: C

Solution :

\[{{x}^{2}}+{{y}^{2}}+6x+6y-2=0\] Centre \[(-3,-3),\]radius \[=\sqrt{9+9+2}\]                 \[=\sqrt{20}\] Now, \[QC=\sqrt{{{(-3)}^{2}}+{{6}^{2}}}=\sqrt{45}\] In right \[\Delta CPQ\] \[PQ=\sqrt{45-20}=5\]