If $r (1 - m^{2}) + m (p - q) = 0$ , then a bisector of the angle between the lines represented by the equation $p x^{2} - 2 r x y + q y^{2} = 0$ , is

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Solution

The correct option is C

Equation of bisectors of angle between the lines represented by $p x^{2} - 2 r x y + q y^{2} = 0$ is

$\frac{x^{2} - y^{2}}{p - q} = \frac{x y}{- r}$

On putting y = mx in (i), we get

$\frac{1 - m^{2}}{p - q} = \frac{m}{- r} \Rightarrow r (1 - m^{2}) + m (p - q) = 0$ .

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