# The Homogeneous Equation of the Second Degree

__General Equation of the Second Degree__

The equation of the form is

When , and are not simultaneously zero, is called the general equation of the second degree or the quadratic equation in and .

__Homogeneous Equation__

An equation of the form is said to be the homogeneous equation of degree , where is a positive integer, and if for some real number , we have

For example, the equation is a homogeneous equation of degree , because

But the general second degree equation

is not homogeneous equation, because

__Second Degree Homogeneous Equation__

The equation of the form is called the second degree homogeneous equation.