Conic sections calculator
Enter a conic equation to identify its type (circle, ellipse, parabola, hyperbola) and find its key properties.
Equation
The four conic sections
Circle: x² + y² = r². All points equidistant from center. Eccentricity = 0.
Ellipse: x²/a² + y²/b² = 1. Oval shape. 0 < e < 1.
Parabola: y = ax² + bx + c. U-shape. e = 1.
Hyperbola: x²/a² − y²/b² = 1. Two branches. e > 1.
How to identify from general form
Ax² + Bxy + Cy² + Dx + Ey + F = 0:
If A = C and B = 0 → Circle. If AC > 0 and A ≠ C → Ellipse. If AC = 0 → Parabola. If AC < 0 → Hyperbola.
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