Editing Degenerate conic (section)

== Classification ==
Over the complex projective plane there are only two types of degenerate conics – two different lines, which necessarily intersect in one point, or one double line. Any degenerate conic may be transformed by a [[projective transformation]] into any other degenerate conic of the same type.

Over the real affine plane the situation is more complicated. A degenerate real conic may be:

* Two intersecting lines, such as <math>x^2-y^2 = 0 \Leftrightarrow (x+y)(x-y) = 0</math> 
* Two parallel lines, such as <math>x^2-1 = 0 \Leftrightarrow (x+1)(x-1) = 0</math> 
* A double line (multiplicity 2),  such as <math>x^2 = 0</math>
* Two intersecting [[complex conjugate line]]s (only one real point), such as <math>x^2+y^2 = 0 \Leftrightarrow (x+iy)(x-iy) = 0</math> 
* Two parallel complex conjugate lines (no real point), such as <math>x^2+1 = 0 \Leftrightarrow (x+i)(x-i) = 0</math> 
* A single line and the line at infinity
* Twice the line at infinity (no real point in the [[affine plane]])

For any two degenerate conics of the same class, there are [[affine transformation]]s mapping the first conic to the second one.