Geo3.11

Find the equation to the pair of angle bisectorsof the pair of lines $(ax+by)^2=3(bx-ay)^2\,$

Simplifying the given pair, we have $x^2(a^2-3b^2)+8abxy+y^2(b^2-3a^2)=0\,$

Therefore,equation to the pair of bisectors of angles between them is $\frac{x^2-y^2}{(a^2-3b^2)-(b^2-3a^2)}=\frac{xy}{4ab}\,$

$ab(x^2-y^2)=(a^2-b^2)xy\,$

$(ax+by)(bx-ay)=0\,$

Therefore,equations to the bisectors are $ax+by=0,bx-ay=0\,$