Which conic section is represented by the following equation? 5 x squared minus x plus 5 y squared minus 3 y minus 12 is equal to 0

The squared terms have equal coefficients: 5x² and 5y², and there is no xy term. A conic with equal coefficients on x² and y² is a circle, provided it represents a real circle. Completing the squares gives (x − 1/2)² + (y − 3/10)² = 2.68, so the radius is real and positive. The equation represents a circle.

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