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(C) The equation of the pair of straight lines joining the origin to the points of intersection is obtained by homogenizing the equation of the curve

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$\pi /3$

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(C) The equation of the pair of straight lines joining the origin to the points of intersection is obtained by homogenizing the equation of the curve using the line equation: $x^2 + y^2 = 4 \left( \frac{x\sqrt{3} + y}{2} ight)^2$ $x^2 + y^2 = 4 \left( \frac{3x^2 + y^2 + 2\sqrt{3}xy}{4} ight)$ $x^2 + y^2 = 3x^2 + y^2 + 2\sqrt{3}xy$ $2x^2 + 2\sqrt{3}xy = 0$ Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 2$,$h = \sqrt{3}$,and $b = 0$. If $\alpha$ is the angle between the lines,then $	an \alpha = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$. $	an \alpha = \frac{2\sqrt{(\sqrt{3})^2 - (2)(0)}}{2 + 0} = \frac{2\sqrt{3}}{2} = \sqrt{3}$. Therefore,$\alpha = \frac{\pi}{3}$.

The angle between the lines joining the origin to the points of intersection of the line $x\sqrt{3} + y = 2$ and the curve $x^2 + y^2 = 4$ is

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