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Q.

Combined equation of pair of lines passing through origin and inclined at 30^o and 60^o respectively with x-axis is

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a

$\sqrt{3}$ y² - x² = 0

b

$\sqrt{3}$ y² +4xy - $\sqrt{3}$ x² = 0

c

$\sqrt{3}$ y² -4xy + $\sqrt{3}$ x² = 0

d

y² - $\sqrt{3}$ x² = 0

answer is D.

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Detailed Solution

$\begin{array}{l} θ_{1} = 30^{\circ}, θ_{2} = 60^{\circ} \\ y = m_{1} x, y = m_{2} x \\ y = \frac{1}{\sqrt{3}} x y = \sqrt{3} x \\ \sqrt{3} y = x, y = \sqrt{3} x \end{array} \begin{array}{l} ∴ (x - \sqrt{3} y) (\sqrt{3} x - y) = 0 \\ \sqrt{3} x^{2} - xy - 3 xy + \sqrt{3} y^{2} = 0 \\ \sqrt{3} x^{2} - 4 xy + \sqrt{3} y^{2} = 0 \end{array}$

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