I am writing a piece of software involving conic sections. I need to write a method that returns a different number (0, 1, 2...) for each type of conic section.
I have determined the following conic sections:
- 0 - Circle
- 1 - Ellipse
- 2 - Parabola
- 3 - Hyperbola
- 4 - Rectangular Hyperbola
and these degenerate conics:
- 5 - Line
- 6 - Point
- 7 - Intersecting Lines
- 8 - Parallel Lines
- 9 - No Graph
My Question: How to determine which of these ten types a given conic section is using only the values of A, B, C, D, E, and F in the equation below:
$$ Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 $$
Thanks in advance for any help, Zach Hilman