Conic Section Identifier Calculator
Result
Classify a quadratic-form discriminant from A, B and C. The output is a sign-based conic type, not a check for degeneracy or real points.
Formula
- Enter quadratic coefficients A, B and C. The tool computes B² − 4AC and labels the result ellipse-type, parabola-type or hyperbola-type by its sign. Since the linear and constant coefficients are not provided, it cannot verify the full conic, detect degenerate cases or guarantee real points. Treat the displayed type as a discriminant classification only.
- The main inputs are A, B, C. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Conic Section Identifier
- A: 1
- B: 0
- C: 1
Using A = 1, B = 0, C = 1, the calculated result is Discriminant: -4 | Type: Ellipse.
Sample result: Calculating…
Frequently asked questions
What does the Conic Section Identifier calculate?
Classify a quadratic-form discriminant from A, B and C. The output is a sign-based conic type, not a check for degeneracy or real points.
Which values should I enter?
Enter A, B, C using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: Discriminant sign test for a real quadratic-plane equation Ax² + Bxy + Cy² + Dx + Ey + F = 0: Δ = B² − 4AC. For a NONDEGENERATE real conic, Δ < 0 indicates ellipse-type, Δ = 0 parabola-type, Δ > 0 hyperbola-type. This calculator only accepts A, B, C and returns the sign-based label. It cannot verify that the full equation is nondegenerate or contains real points, because D, E and F are not entered. Zero or all-zero quadratic coefficients may therefore receive a misleading label..
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.