Directrix

Definition

A directrix is a fixed line used in the description of a curve or surface, such as a parabola, ellipse, or hyperbola. It helps define the locus of points that form these conic sections.

5 Must Know Facts For Your Next Test

1. For a parabola, the distance from any point on the parabola to the directrix is equal to its distance to the focus.
2. Ellipses and hyperbolas have two directrices, one corresponding to each focus.
3. In polar coordinates, equations involving conic sections can be derived using the directrix and eccentricity.
4. The general equation for a conic section can incorporate the directrix by using its distance formula.
5. Directrices are perpendicular to the major axis in an ellipse and hyperbola.

Review Questions

• What is the relationship between a point on a parabola and its directrix?
• How many directrices does an ellipse have?
• Explain how you would use a directrix to derive the equation of a conic section in polar coordinates.

Related terms

Focus: A fixed point used with the directrix to define a conic section.

Eccentricity: A parameter that determines how much a conic section deviates from being circular.

Latus Rectum: A line segment perpendicular to the axis of symmetry of a conic section that passes through the focus.