A pair of straight line intersect on y axis

Question

If the pair of lines ax²+2hxy+by²+2gx+2fy+c=0 intersect on the y-axis then 

Answer 1

Solution: Put x=0 in the given equation

=>by²+2fy+c=0

For unique point of intersection.

f²−bc=0

=>af²−abc=0

Since abc+2fgh−af²−bg²−ch²=0

=> 2fgh−bg²−ch²=0

Hence A is the correct answer.