question_answer

Area of triangle formed by common tangents to the circle \[{{x}^{2}}+{{y}^{2}}-6x=0\] and\[{{x}^{2}}+{{y}^{2}}+2x=0\] is-

A) \[3\sqrt{3}\]                            

B) \[2\sqrt{3}\]

C) \[9\sqrt{3}\]                            

D) \[6\sqrt{3}\]

Correct Answer: A

Solution :

 A divides \[{{C}_{1}}{{C}_{2}}\] externally in the ratio\[1:3\]. \[\therefore \]coordinate of\[A\]are\[(-3,\,\,0)\] We have\[\sin \theta =1/2\]\[\therefore \]\[\theta ={{30}^{o}}\] Area\[=3\times 3\tan {{30}^{o}}=3\sqrt{3}\]