12.2 Parabolas

Ideas in this lesson

Vertices and orientation

One coordinate is squared. Its positive coefficient and the signed focal parameter determine the opening direction.

Focus and directrix

A parabola contains points equidistant from its focus and directrix; the focal parameter is signed.

Directrices

For a vertical parabola, the directrix is one signed focal parameter below the vertex; it lies opposite the focus.

Write a parabola equation

The squared-coordinate side equals four times the signed focal parameter times the unsquared shifted coordinate.

Focal widths

The latus rectum passes through the focus perpendicular to the axis and has length four times the absolute focal parameter.