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 \[=\frac{1}{2}\times 4\times \sqrt{3}=2\sqrt{3}\].