## 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.