The area (in sq units) of the triangle formed | vedclass

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(C) The equation of the circle is $x^2+y^2=4$. The point $P(1, \sqrt{3})$ lies on the circle.The equation of the tangent at $P(x_1, y_1)$ is $xx_1 + y

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$2 \sqrt{3}$

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(C) The equation of the circle is $x^2+y^2=4$. The point $P(1, \sqrt{3})$ lies on the circle.The equation of the tangent at $P(x_1, y_1)$ is $xx_1 + yy_1 = r^2$,which is $x(1) + y(\sqrt{3}) = 4$,or $x + \sqrt{3}y = 4$.The tangent meets the $X$-axis at $A(4, 0)$.The normal at $P(1, \sqrt{3})$ passes through the origin $O(0, 0)$ and has the equation $y = \sqrt{3}x$.The triangle is formed by the points $O(0, 0)$,$P(1, \sqrt{3})$,and $A(4, 0)$.The area of $	riangle OPA = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes OA 	imes y_P = \frac{1}{2} 	imes 4 	imes \sqrt{3} = 2 \sqrt{3}$ sq units.

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

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