Conic Section Analyzer

Classify and graph a conic from its equation

4x² + 0xy + 9y² + 0x + 0y + -36 = 0

Conic type

Ellipse

Discriminant (B² − 4AC)

-144

Matrix determinant

-1,296

Center

(0, 0)

Axis rotation

180°

Semi-major axis (a)

Semi-minor axis (b)

Eccentricity

0.7454

Focal distance (c)

2.2361

Foci

(-2.2361, 0) (2.2361, 0)

Vertices

(-3, 0) (3, 0)

About this calculator

The Conic Section Analyzer classifies any general second-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0 as a circle, ellipse, parabola, hyperbola, or a degenerate point or line pair. It uses the discriminant B² − 4AC and the conic matrix determinant, then reports the center, rotation, semi-axes, eccentricity, foci, vertices, focus and directrix, and graphs the curve.