# The Second Degree Homogeneous Equation Represents a Pair of Lines

As we know that the equation of the form is called the second degree homogeneous equation, the second degree homogeneous equation represents the pair of straight lines passing through the origin.

The second degree homogeneous equation is given as

This equation (i) can be rewritten in the form

Considering the above equation (ii) as a quadratic equation in terms of and using the quadratic formula to solve this equation, we have

Let and

Making these substitutions, equations (iii) are and , which are obviously equations of lines passing through the origin because there are no y-intercepts in these equations (iii).

This shows that the second degree homogeneous equation represents the pair of straight lines passing through the origin.