Question

The combined equation of the lines $l_1,l_2$ is $2x^2+6xy+y^2=0$ and that of the lines $m_1,m_2$ is $4x^2+18xy+y^2=0$. If the angle between $l_1$ and $m_2$ be $\alpha$ then the angle between $l_2$ and $m_1$ will be

• A. $\frac{\pi }{2}-\alpha$
• B. $2\alpha$
• C. $\frac{\pi }{4}+\alpha$
• D. $\alpha$

Answer 1

The correct option is D $\alpha$

The combined equation of bisector angles between the lines of the first pair is

$\frac{x_2-y_2}{a-b}=\frac{xy}{h}$
so,$\frac{x^2-y^2}{2-1}=\frac{xy}{3}$ ------------(1)
and that of other pair is
$\frac{x^2-y^2}{4-1}=\frac{xy}{9}$ -------------(2)
As these equations are the same,
Therefore the two pairs are equally inclined to each other