If the pair of lines $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ intersect on the y-axis, then prove that $2 f g h = b g^{2} + c h^{2}$

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If the pair of lines

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

intersect on the y-axis, then prove that

2 f g h = b g^{2} + c h^{2}

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Question Text

If the pair of lines

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

intersect on the y-axis, then prove that

2 f g h = b g^{2} + c h^{2}

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