$Two pairs of lines 2x^2+6xy+y^2=0 and 4x^2+18xy+y^2= 0$

$The angular bisector of a{x}^2+2hxy+b{y}^2= 0 is h\left(x^2-y^2\right)-xy\left(a-b\right)=0$

$The angular bisector of 2x^2+6xy+y^2= 0 is 3x^2-xy-3y^2=0$

$The angular bisector of 4x^2+18xy+y^2=0 is 9x^2-3xy-9y^2=0$

$The above two equations represents same set of pair of lines$

$it means both the pair of lines possess same angualr bisectors$