Focus

Definition

In the context of conic sections, a focus is one of the points used to define and construct an ellipse or a parabola. The distance from any point on the conic section to the focus has specific geometric properties.

5 Must Know Facts For Your Next Test

1. The plural of focus is foci.
2. In an ellipse, there are two foci, and the sum of the distances from any point on the ellipse to both foci is constant.
3. For a parabola, there is one focus and it lies on the axis of symmetry.
4. The distance between a point on a parabola and its focus equals the perpendicular distance from that point to the directrix.
5. In polar coordinates, conic sections can be represented using equations involving the distance from a focus.

Review Questions

• How many foci does an ellipse have?
• What geometric property defines how distances relate to the focus in a parabola?
• Describe how you would locate the foci of an ellipse given its major and minor axes.

Related terms

Ellipse: A set of all points for which the sum of distances to two fixed points (foci) is constant.

Parabola: A set of all points equidistant from a single point called the focus and a line called the directrix.

Directrix: A fixed line used in describing a curve or surface, particularly in defining parabolas.