Question

How do you to tell the difference between an ellipse, hyperbola, parabola, or circle if all are in standard form?

Answer 1

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.