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Conic Section Classifier — result sheet
Classify a nonrotated quadratic conic from the x-squared, xy, and y-squared coefficients.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Quadratic discriminant Δ = B²−4AC; Δ<0 indicates ellipse-like, Δ=0 parabola-like, and Δ>0 hyperbola-like behavior.
The quadratic part determines the broad conic family; linear and constant terms are needed for location and degeneracy checks, which this classifier does not attempt.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- x² coefficient A — minimum -1000000; maximum 1000000
- xy coefficient B — minimum -1000000; maximum 1000000
- y² coefficient C — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| x² coefficient A | 1 |
| xy coefficient B | 0 |
| y² coefficient C | 1 |
Δ = −4; ellipse-like quadratic part.
Assumptions and limits
- At least one quadratic coefficient is nonzero.
- The classification is based only on the quadratic part and may not distinguish degenerate cases.
- The result does not determine rotation, center, focus, or real-point existence.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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