Step-by-step explanation:
General form of a conic section is:
Ax² + Bxy + Cy² + Dx + Ey + F = 0
If B = 0:
Parabola: Either x² or y² term, but not both
Circle: x² and y² have the same coefficient
Ellipse: x² and y² have different positive coefficients
Hyperbola: x² and y² have different signs
Otherwise, look at the discriminant.
If B² − 4AC < 0, then the conic is an ellipse.
If B² − 4AC = 0, then the conic is a parabola.
If B² − 4AC > 0, then the conic is a hyperbola.
