# How do you identify conic sections?

Sep 28, 2014

General form of the conic equation

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

The coefficients $A$ and $C$ are need to identify the conic sections without having to complete the square.

$A$ and $C$ cannot be $0$ when making this determination.

Parabola$\to A \cdot C = 0$

Circle$\to A = C$

Ellipse$\to A \cdot C > 0 \mathmr{and} A \ne C$

Hyperbola$\to A \cdot C < 0$