Definition:Homogeneous Quadratic Equation

This page is about Homogeneous Quadratic Equation. For other uses, see Homogeneous.

Definition

A homogeneous quadratic equation is a quadratic equation in two variables such that each term is of degree $2$:

$a x^2 + h x y + b y^2 = 0$

Also presented as

Some older sources present this as:

$a x^2 + 2 h x y + b y^2 = 0$

The $2$ in the coefficient of $x y$ can make some of the algebra more simple further down the line.

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $15$. The homogeneous equation of second degree