Which conic section is represented by the following equation? 3 x squared minus 7 x plus 8 y squared minus 2 y plus 1 is equal to 0

The squared terms are 3x² and 8y², so their coefficients have the same sign but are unequal. That pattern represents an ellipse (a circle would have equal coefficients). Completing the squares also gives a real ellipse: 3(x − 7/6)² + 8(y − 1/8)² = 77/24. Therefore, the conic is an ellipse.

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