The equation of bisectors of the angle between the lines represented by 3 x 2 - 5 x y + 4 y 2 = 0 is

Given equation is  $3x^2-5xy+4y^2=0 .....\left(1\right)$

Compare the given equation with $a{x}^2+2hxy+b{y}^2=0 ......\left(2\right)$

We get, $a=3$$, 2h=-5$ and $b=4$

Now the equation of the bisector of the angle between the pair of lines $\left(1\right)$  is

$\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

$\Rightarrow \frac{x^2-y^2}{3-4}=\frac{xy}{{\displaystyle \frac{-5}{2}}}$

$\Rightarrow 5x^2-2xy-5y^2=0$

$\Rightarrow 5\left(x^2-y^2\right)=2xy$