question_answer

Area of triangle formed by common tangents to the circle \[{{x}^{2}}+\text{ }{{y}^{2}}-6x=0\] 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\[=3\times 3\tan {{30}^{o}}=3\sqrt{3}\]