Which conic section is represented by the following equation?–5x2 + 10xy – 5y2 + 2x – y + 4 = 0

For a conic written as Ax² + Bxy + Cy² + Dx + Ey + F = 0, compare B² − 4AC with zero. Here A = −5, B = 10, and C = −5, so B² − 4AC = 10² − 4(−5)(−5) = 100 − 100 = 0, which identifies a parabola. Therefore, the correct choice is C, parabola.

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