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Q.
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 $(1, \sqrt{3})$ is
Conic Sections
Solution:
The equations of the tangent and the normal to
$x^{2}+y^{2}=4$ at $(1, \sqrt{3})$ are, respectively,
$x+\sqrt{3} y=4$ and $y=\sqrt{3} x$
The tangent meets the $x$-axis at $(4,0)$. Therefore,
Area of $\triangle O A P=\frac{1}{2}(4) \sqrt{3}$
$=2 \sqrt{3}$ sq. units
