Conic Section Identifier Calculator
The Conic Section Identifier classifies a general second-degree equation as an ellipse, parabola, or hyperbola using the discriminant B² − 4AC. Enter the coefficients A, B, and C.
Formula
Discriminant = B² − 4AC: < 0 ellipse, = 0 parabola, > 0 hyperbola
- A circle is a special ellipse where A = C and B = 0.
- The discriminant classifies the conic regardless of the linear terms.
A=1, B=0, C=1
Inputs
- A (x² coefficient): 1
- B (xy coefficient): 0
- C (y² coefficient): 1
Discriminant = 0 − 4 = −4 < 0, and A = C, so it is a circle.
Frequently asked questions
How do you identify a conic section?
Compute B² − 4AC: negative is an ellipse, zero a parabola, and positive a hyperbola.