Question

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

• A. $2\sqrt{3}$
• B. $\sqrt{3}$
• C. $4\sqrt{3}$
• D. None of these

Answer 1

The correct option is A $2\sqrt{3}$

Equation of circle is $x^2+y^2=4$

Equation of tangent at $(1,\sqrt{3})$ is $T\equiv x+\sqrt{3}y-4=0$

Base of the triangle is $4$and height is $\sqrt{3}$
Hence the required area is
$=\frac{1}{2}\times 4\times \sqrt{3}=2\sqrt{3}$