Prove that two of the lines represented by the equation $$ay^4+bxy^3+cx^2y^2+dx^3y+ex^4=0$$will be perpendicular if $$(b+d)(ad+be)+(e-a)^2(a+c+e)=0$$
I tried to solve the equation by assuming two arbitrary pairs of line $$(ay^2+ex^2+2hxy)(x^2-pxy+y^2)$$ so as to make the second pair that of perpendicular lines. (I assumed $h$ and $p$ arbitrarily)
I then multiplied the terms in the bracket and by comparing the terms found the value of $h$ and $p$, but I couldn't get any equation which would lead to the required condition.
Can anybody just give me a small hint as to how can i advance further.