If two lines represented by x4+x3y+cx2y2−xy3+y4=0 bisect the angle between the other two, then the value of c is

Since the product of the slope of the four line represented by the given equation is 1 and a pair of lines represents the bisectors of the angles between the other two, the product of the slopes of each pair is  -1. so, let the equation of one pair be ax2+2hxy−ay2=0. Then the equation of its bisectors is x2−y22a=xyh by hypothesis, x4+x3y+cx2y2−xy3+y4=(ax2+2hxy−ay2)(hx2−2axy−hy2)=ah(x4+y4)+2(h2−a2)(x3y−xy3)−6ahx2y2