If the slope of one of the lines represented by ax2+2hxy+hy2=0 is the square of the other, then a+bh+8h2ab=

Let m and m2 be the slopes of the lines represented by ax2+2hxy+by2=0.Then, m+m2=−2hb and mm2=ab or m3=ab Now, (m+m2)3=(−2hb)3∴m3+m6+3mm2(m+m2)=−8h3b3∴ab2(a+b)+8h3b3=6ahb2∴a+bh+8h2ab=6These are the set of parallel lines and the distance between parallel lines are equal. So, the figure is a rhombus.