Conic Sections Cheat Sheet
General Equation Features
The general equation of a conic section is
The discriminant is the number
On the Curve
Vertex: an extreme point or turning point
Not on the Curve
Focus: a point used to define the conic section, the curve bends around this point. (Plural: foci)
Directrix: a straight line used to define the conic section. (Plural: directrices)
A conic section is the set of all points P such that the distance from P to the nearest focus is a constant multiple of the distance from P to the nearest directrix.
The eccentricity e of a conic section is the distance from any point P on the curve to the nearest focus, divided by the distance from P to the nearest directrix.
A Note About Circles
A circle is a special type of ellipse, where A = B in the general conic equation. For a circle,
Eccentricity is defined as e = 0.
The center is the focus.
There are no directrices.
There are no vertices.
Since the eccentricity of a circle is 0, the eccentricity of a conic can be thought of as how much the curve deviates from being circular.