First slide

Pair of straight lines

Question

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

Moderate

A

$\frac{π}{2} - α$
B

$2 α$
C

$\frac{π}{4} + α$
D

$α$

Solution

The combined equation of bisectors of angle between the lines of first pair and second pair are same which is $3 (x^{2} - y^{2}) = (2 - 1) x y$
therefore two pairs are equally inclined to each other

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