Which equation represents an ellipse?

For a conic Ax² + Bxy + Cy² + … = 0, B² − 4AC < 0 indicates an ellipse-type conic. In choice C, A = 3, B = 7, and C = 8, so B² − 4AC = 49 − 96 = −47. Completing the square confirms it has real points, so choice C, “3x² + 7xy + 8y² + 3x − 9y + 5 = 0,” represents an ellipse.

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