The equation ax^2 + 2y^2 + 2bxy + 2x - y + c | vedclass

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(D) For a general second-degree equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ to represent a circle,the following conditions must be met:$1$. The coe

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$a = 2, b = 0, c = 0$

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(D) For a general second-degree equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ to represent a circle,the following conditions must be met:$1$. The coefficient of $x^2$ must equal the coefficient of $y^2$,so $a = 2$.$2$. The coefficient of $xy$ must be zero,so $2b = 0$,which implies $b = 0$.$3$. Since the circle passes through the origin $(0, 0)$,the constant term $c$ must be $0$.Thus,the values are $a = 2, b = 0, c = 0$.

The equation $ax^2 + 2y^2 + 2bxy + 2x - y + c = 0$ represents a circle passing through the origin,if:

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