JEE Advanced Mathematics question

If the pair of lines ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on the -axis then

Answer: (A),(B)

Solution

Since it is a pair of lines, abc+2fgh-af^2-bg^2-ch^2=0 … (1). Let the intersection be . It satisfies and , so

hλ+g=0, bλ+f=0\ ⇒\ λ=- fb\ ⇒\ fh=bg \text{…

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Question ID VK-108882