Directrix

Definition

A directrix is a fixed line used in the geometric definition of a conic section. For a parabola, it is equidistant from any point on the curve to the focus and the directrix.

5 Must Know Facts For Your Next Test

1. A parabola can be defined as the set of all points equidistant from a single point (the focus) and a line (the directrix).
2. The equation of a parabola with vertex at $(h, k)$ and directrix $y = k - p$ is given by $(x - h)^2 = 4p(y - k)$.
3. In polar coordinates, the directrix helps define conic sections by its distance from the pole.
4. The distance between any point on the parabola and the directrix is equal to its distance from the focus.
5. For hyperbolas and ellipses, there are two directrices corresponding to each focal axis.

Review Questions

• What is the relationship between any point on a parabola and its directrix?
• How does the equation of a parabola change based on its directrix?
• In what way does the concept of a directrix apply to other conic sections like ellipses and hyperbolas?

Related terms

Focus: A fixed point used in defining conic sections; for parabolas, it is equidistant from any point on the curve to this point and the directrix.

Conic Sections: Curves obtained by intersecting a plane with a double-napped cone; includes parabolas, ellipses, and hyperbolas.

Vertex: The highest or lowest point on a parabola; it lies midway between the focus and the directrix.