Question

Find the joint equation of bisectors of the angles between the lines represented by $5x^2+6xy-y^2=0$.

Answer 1

Equation of lines is $5x^2+6xy-y^2=0$

comparing above equation with $a{x}^2+2hxy+b{y}^2=0$

$a=5,h=3,b=-1$

Combined equation of pair of angle bisectors of given lines is $\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

$\frac{x^2-y^2}{5-(-1)}=\frac{xy}{3}$

$\frac{x^2-y^2}{6}=\frac{xy}{3}$

$x^2-2xy-y^2=0$.