The combined equation of the lines $l_1,l_{2}is2x^2+6xy+y^2=0$ and that of the lines $m_1,m_{2}is4x^2+18xy+y^2=0.$ If the angle between $l_{1}and{m}_{2}be\text{'}\alpha \text{'}thenanglebetween{l}_{2}and{m}_{1}is$

Given Equation $2x^2+6xy+y^2=0--\left(i\right)$

 $4x^2+18xy+y^2=0---\left(ii\right)$

Angle bisector of (i)  $3\left(x^2-y^2\right)=\left(2-1\right)xy$ 

                                   $\Rightarrow 3x^2-xy-3y^2=0$

Angle bisector of (ii) $9\left(x^2-y^2\right)=\left(4-1\right)xy$

                                  $\Rightarrow 3x^2-xy-3y^2=0$

Angle bisectors are Equal

The lines are Equally inclined to each other

 $\begin{array}{l}If\text{'}\alpha \text{'}istheanhleb/w{l}_{1}and{l}_2\\ Thenangleb/w{l}_{2}and{m}_{1}isalso\text{'}\alpha \text{'}\end{array}$