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)
3
Semi-minor axis (b)
2
Eccentricity
0.7454
Focal distance (c)
2.2361
Foci
(-2.2361, 0) (2.2361, 0)
Vertices
(-3, 0) (3, 0)
Conic Section AnalyzerGraph of the conic section, classified as a Ellipse, plotted on x and y axes with its center, foci, vertices and other key features marked.

この計算機について

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.