If the line lx+my+n=0 intersects the curve ax2+2hxy+by2=1at P and Q such that the circle with PQ as a diameter passes through the origin, then l2+m2=

It is given that the circle with PQ as a diameter passes through the origin. This means that symbol ∠POQ=90∘ i.e. the lines joining the origin to the points of intersection of ax2+2hxy+by2=1 and 1x+my+n=0 are at right angle.The combined equation of OP and OQ is given byax2+2hxy+by2=1x+my−n2This represents a pair of perpendicular lines.∴  Coeff. of x2+ Coeff. of y2=0⇒ an2−l2+bn2−m2=0⇒l2+m2=(a+b)n2