Which conic section is represented by the following equation?5x2 – x + 5y2 – 3y – 12 = 0

The coefficients of x² and y² are equal (both 5), and there is no xy term, which identifies a circle. Completing the squares confirms it is a real circle: 5(x − 1/10)² + 5(y − 3/10)² = 49/4. Therefore, the equation represents a circle.

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