A point $P (\sqrt{3}, 1)$ moves on the circle $x^{2} + y^{2} = 4$ and after covering a quarter of the circle leaves it tangentially. The equation of a line along which point moves after leaving the circle is

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$y = \sqrt{3} x + 4$

$\sqrt{3} y = x + 4$

$\sqrt{3} y = x - 4$

$y = \sqrt{3} x - 4$

answer is B, C.

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Detailed Solution

$\begin{array}{l} x^{2} + y^{2} = 4 \Rightarrow r = 2; ∠ XOA = - 60^{0} \\ A = (0 + 2 (+ \frac{1}{2})), 0 + 2 (- \frac{\sqrt{3}}{2}) \Rightarrow A = (1, - \sqrt{3}) \end{array}$

Equation of tangent at A is $\sqrt{3} y = x - 4$

$∠ BOX = 120^{\circ} \Rightarrow B = (- 1, \sqrt{3})$

Equation of tangent at B is $\sqrt{3} y = x + 4$

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