Question

The area of the triangle formed by the positive X-axis and the normal and tangent to the circle $x^2+y^2=4$ at $(1,\sqrt{3})$ in sq. units is:

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $2\sqrt{3}$
• D. $3\sqrt{3}$

Answer 1

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

the tangent of $x^2+y^2=4$ at $(1,\sqrt{3})is\sqrt{3}y+x=4$ and that of normal is $y=\sqrt{3}x$
So, the area of
${△}^{le}=1/2\times 4\times \sqrt{3}=2\sqrt{3}squnits$