Identify the type of conic section from its general quadratic equation.
General Equation
Ax² + Bxy + Cy² + Dx + Ey + F = 0
Classification
Conic TypeCircle
Discriminant (Δ)-4.00
About this calculator
Conic Sections
Conic sections are curves obtained by intersecting a cone with a plane. The general equation of a conic is Ax² + Bxy + Cy² + Dx + Ey + F = 0. The type of conic is largely determined by the discriminant B² - 4AC.
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Pro Tips
Δ < 0: Ellipse (or Circle if A=C and B=0)
Δ = 0: Parabola
Δ > 0: Hyperbola
Degenerate cases (like point, line, or intersecting lines) occur if the determinant of the full 3x3 matrix is zero.
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Fun Facts
"Kepler discovered that planetary orbits are ellipses with the Sun at one focus."
"Hyperbolas are used in navigation systems like LORAN."
"The satellite dish in your home receives signals by focusing them to a point using a parabolic shape."
