Directrix

Definition

A directrix is a fixed line used in the definition of a conic section. In the context of parabolas, it is used to define the set of points equidistant from a given point (focus) and the line (directrix).

5 Must Know Facts For Your Next Test

1. The general equation for a parabola can be written as $y = ax^2 + bx + c$.
2. For any point on a parabola, the distance to the focus is equal to its distance to the directrix.
3. In polar coordinates, conic sections including parabolas can also be defined using a directrix.
4. The vertex of a parabola is equidistant from both the focus and the directrix.
5. The equation of a vertical parabola with vertex at $(h,k)$ and focus at $(h,k+p)$ is $(x-h)^2 = 4p(y-k)$.

Review Questions

• What role does the directrix play in defining a parabola?
• How do you find the equation of a parabola given its vertex and directrix?
• Explain how the distances from any point on the parabola to the focus and directrix are related.

Related terms

Focus: A fixed point used with a directrix to define a conic section; for parabolas, each point is equidistant from this point and its corresponding directrix.

Vertex: The midpoint between the focus and directrix of a parabola; it represents the highest or lowest point on a graph depending on its orientation.

Axis of Symmetry: $\text{A line that divides}$\ \text{the graph of}$\ \text{a}$$\parabola into two mirror-image halves}.