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The equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represents a circle, the condition will be

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a=b and c=0

f=g and h=0

a=b and h=0

f=gand c=0

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detailed solution

Correct option is C

Comparing ax2+2hxy+by2+2gx+2fy+c=0 with x2+y2+2gx+2fy+c=0 we find that the given equation will represent a circle if a=b and h=0

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The equation ax2+2hxy+by2+2gx+2fy+c=0 represents a circle, the condition will be

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The equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ represents a circle, the condition will be