Latus rectum

Definition

The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry that passes through the focus and whose endpoints lie on the parabola. It is used to describe certain geometric properties of parabolas.

5 Must Know Facts For Your Next Test

1. The length of the latus rectum of a parabola $y^2 = 4ax$ is $4a$.
2. For a parabola $x^2 = 4ay$, the length of the latus rectum is also $4a$.
3. The endpoints of the latus rectum are equidistant from the focus of the parabola.
4. The latus rectum can be used to determine other important features, such as directrix and vertex relationships in parabolas.
5. In terms of coordinates, if the equation of a parabola is $y^2 = 4ax$, then its focus is $(a,0)$ and its latus rectum endpoints are $(a, 2a)$ and $(a, -2a)$.

Review Questions

• What is the length of the latus rectum for a parabola given by $x^2 = -12y$?
• How do you find the endpoints of the latus rectum for a given parabolic equation?
• Explain how to use the latus rectum to find distances from the focus to other points on a parabola.

Related terms

Focus: A fixed point on the interior of a parabola used in its definition and construction.

Directrix: A fixed line used in conjunction with a focus to define a parabola; every point on a parabola is equidistant from both.

Axis of Symmetry: A line through which an object or shape can be mirrored symmetrically; for parabolas, it passes through both vertex and focus.