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Directrix

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Algebra and Trigonometry

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).

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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.
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