Some Useful Terms of Conic Sections

Before deriving equations, it helps to fix the vocabulary that is common to every conic section — parabola, ellipse and hyperbola alike. These seven terms will be used constantly for the rest of the chapter:

1. Axis — a line about which the conic section is symmetric (a mirror line for the curve) is called an axis of the conic.
2. Vertex — a point where the conic meets its own axis of symmetry is called a vertex.
3. Focal distance — for any point on the conic, its distance from the focus is called the focal distance of that point.
4. Focal chord — any chord (a line segment joining two points of the curve) that passes through the focus is called a focal chord.
5. Latus rectum — a focal chord that is perpendicular to the axis of symmetry is called the latus rectum. (Its length is one of the most useful measurements of a conic's "width" at the focus, and is computed for every conic in this chapter.)
6. Centre of a conic — the point that bisects every chord of the conic passing through it is called the centre. (A parabola, notably, has no such point — only the ellipse and hyperbola have a true centre.) …