If the slope of one of the lines represented by ax2+2hxy+by2=0 be the square of the other, then a+bh+8h2ab is equal to

We can write yx2+2hbyx+ab=0If the slopes of the lines are m and m2 thenm+m2=−2hb and mm2=ab⇒ab1/3+ab2/3=−2hb⇒ab+ab2+3ab−2hb=−8h3b3⇒ab2[b+a−6h]+8h3b3=0⇒a+b−6h+8h3ab=0⇒a+bh+8h2ab=6.