Latus rectum

Definition

The latus rectum of a parabola is a line segment perpendicular to the axis of symmetry that passes through the focus. It has endpoints on the parabola itself.

5 Must Know Facts For Your Next Test

1. The length of the latus rectum is $4p$, where $p$ is the distance from the vertex to the focus.
2. In standard form, for a parabola $y^2 = 4px$, the latus rectum lies parallel to the y-axis.
3. For a parabola opening upwards or downwards, such as $x^2 = 4py$, the latus rectum lies parallel to the x-axis.
4. The endpoints of the latus rectum can be found by adding and subtracting $2p$ from the coordinate of the focus.
5. The concept of latus rectum helps in understanding properties related to focal width and directrix.

Review Questions

• What is the length of the latus rectum for a parabola with equation $y^2 = -8x$?
• Describe how you would find the endpoints of the latus rectum for a given parabola.
• How does knowing the latus rectum help in graphing a parabola?

Related terms

Focus: A fixed point used to define and construct a parabola; located inside its curve.

Directrix: A fixed line used in conjunction with a focus to define a parabola.

Axis of Symmetry: \A line that vertically or horizontally bisects a parabola into two mirror-image halves.