Let $u = a x + b y + a \sqrt[3]{b} = 0, v = b x - a y + b \sqrt[3]{a} = 0$ be two straight lines. The equation of the bisectors of the angle formed by $L_{1} \equiv (\tan θ_{1}) u - (\tan θ_{2}) v = 0$ and $L_{2} \equiv (\tan θ_{1}) u + (\tan θ_{2}) v = 0 for θ_{1}, θ_{2} \in (0, \frac{π}{2})$ is

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$(\tan θ_{2}) u - (\tan θ_{1}) v = 0$

$v = 0$

$u = 0$

$(\tan θ_{2}) u + (\tan θ_{1}) v = 0$

answer is A, D.

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Detailed Solution

Note that lines $u = 0, v = 0$ are perpendicular.

Make the co-ordinate axes coincide with $u = 0$

$v = 0 .$

Now the lines $L_{1} \equiv 0, L_{2} \equiv 0$ are equally

inclined with UV-axes

$∴ u = 0, v = 0$ are bisectors.

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