Types

There are 2 definitions for a conic section.

Cone Definition

Family of curves that can be formed by the intersection of a cone with a plane.

Based on two points (foci) and their distances ( $r, r^{'}$ ) to the curve.

r + r^{'} = k

r + r^{'} = 2 a

∣ r - r^{'} ∣ = k

r = r^{'}

Conic sections can also be defined by the ratio, or eccentricity $e$ of the distance from a focus (fixed point) to a directrix (fixed line).

e = \frac{FP}{QP}

Using the focus and directrix, we get a new equation for conic sections:

r = \frac{e d}{1 + e cos θ} .