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The combined equation of the two lines $a x + b y + c = 0$ and $a' x + b' y + c' = 0$ can be written as $(a x + b y + c) (a' x + b' y + c') = 0 .$ The equation of the angle bisectors of the lines represented by the equation $2 x^{2} + x y - 3 y^{2} = 0$ is

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$3 x^{2} + 5 x y + 2 y^{2} = 0$

$x^{2} - y^{2} - 10 x y = 0$

$3 x^{2} + x y - 2 y^{2} = 0$

$x^{2} - y^{2} + 10 x y = 0$

answer is B.

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Detailed Solution

Pair of angular bisector equation $\frac{x^{2} - y^{2}}{2 - (- 3)} = \frac{xy}{\frac{1}{2}}$
$\Rightarrow$ x² - y² - 10xy = 0

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