Conics
There are serveral definitions possible to what a conic precisely is.
Here we define a conic as all points with a fixed ratio r between the distance of a point to a line and the distance of that point to a fixed point.
We choose the line to be x=d and the ratio to be c. By varying r and d we can find the connics point, circle, ellips, parabola, hyperbole and crossing lines.