JEE Main & Advanced
Mathematics
Circle and System of Circles
Question Bank
Tangent and normal to a circle
question_answer
The area of triangle formed by the tangent, normal drawn at \[(1,\sqrt{3})\]to the circle \[{{x}^{2}}+{{y}^{2}}=4\]and positive x-axis, is [IIT 1989; RPET 1997, 99; Kurukshetra CEE 1998]
A) \[2\sqrt{3}\]
B) \[\sqrt{3}\]
C) \[4\sqrt{3}\]
D) None of these
Correct Answer:
A
Solution :
\[T\equiv x+\sqrt{3}y-4=0\] Hence the required area \[=\frac{1}{2}\times 4\times \sqrt{3}=2\sqrt{3}\].