Example of Finding the Angle Between the Lines Represented by the Second Degree Homogeneous Equation
Find the lines represented by the second degree homogeneous equation . Also find the measure of the angle between them.
We have the second degree homogeneous equation:
Calculating the factors of the given equation:
This represents the required equations of straight lines passing through the origin.
Now let be the required angle between this pair of lines, and we have
Compare with the general equation of a homogeneous equation .
Here . If is the angle between the pair of lines, then