JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-37
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\[=3\times 3\tan {{30}^{o}}=3\sqrt{3}\]