The gradient of one of the line of ax2+2hxy+by2=0 is twice that of the other,show that 8h2=9ab

Answer 1

what do you mean by

one of the line of ax2+2hxy+by2=0

?? That is a conic section, unless it's degenerate. In that case, you have

(ax+c)(x+d)=0
ad+c = 2h
cd = b

Now work with the slopes of the lines, using the condition that one is twice the other.

Answer 2

Saani