The equation $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ will represent a circle, if

a = b = 0 and c = 0

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f = g and h = 0

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a = b ≠ 0 and h = 0

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f = g and c = 0

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Solution

The correct option is C a = b ≠ 0 and h = 0
We know that the equation $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ will represent a circle, if a = b ≠ 0 and h = 0
It is a fundamental concept.

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