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If the equation $a x^2+b y^2+2 h x y+2 g x+2 f y+c=0$ represents a circle passing through the origin, then
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$a=b, h=c=0$
The standard equation of circle which passes through origin is $x^2+y^2+2 g x+2 f y=0$
If the equation $a x^2+b y^2+2 h x y+2 f y+c=0$ represent a circle passing through origin, then $a=b, h=0, c=0$.
If the equation $a x^2+b y^2+2 h x y+2 f y+c=0$ represent a circle passing through origin, then $a=b, h=0, c=0$.
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