The combined equation of the lines $l_{1}$ and $l_{2}$ is $2 x^{2} + 6 x y + y^{2} = 0$ and that of the lines $m_{1}$ and $m_{2}$ is $4 x^{2} + 18 x y + y^{2} = 0$ . If the angle between $l_{1}$ and $m_{2}$ is $α$ , then the angle between $l_{2}$ and $m_{2}$ will be

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$\frac{π}{4} + α$

$α$

$\frac{π}{2} - α$

$2 α$

answer is D.

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Detailed Solution

The combined equation of the bisectors of angles between the lines of the first pair is $\frac{x^{2} - y^{2}}{2 - 1} = \frac{x y}{9}$ As these equation are the same, the two pairs are equally inclined to each other.

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