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Find Parabola With Focus and Directrix Calculator Online

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Understanding parabolas and their mathematical representations can be challenging, especially when dealing with specific forms like the vertex form. The Find Parabola With Focus and Directrix Calculator is a powerful tool designed to simplify these complexities, providing users with an efficient way to determine the key elements of a parabola, such as the vertex, focus, and directrix.

Formula

  1. Vertical Parabola:
    • Vertex form: (xh)2=4p(yk)
    • Focus: (h,k+p)
    • Directrix: y=kp
  2. Horizontal Parabola:
    • Vertex form: (yk)2=4p(xh)
    • Focus: (h+p,k)
    • Directrix: x=hp

Where:

  • (h,k) is the vertex of the parabola.
  • p is the distance from the vertex to the focus (and from the vertex to the directrix).
  • If the parabola is vertical, it opens upward or downward. If horizontal, it opens left or right.
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General Terms Table

Here’s a handy table of general terms that people commonly search for:

TermMeaning
VertexThe point (h, k) on the parabola.
FocusThe focal point of the parabola.
DirectrixThe line that is equidistant from all points on the parabola.
ParabolaA U-shaped curve formed by the intersection of a cone with a plane parallel to its side.

Example

Let’s consider an example to illustrate the practical application of the calculator.

Suppose we have a vertical parabola with a vertex at (3, 4) and a focus at (3, 7). Using the calculator, we can find the directrix, equation, and other essential parameters effortlessly.

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Most Common FAQs

Q: What is the vertex of a parabola?

A: The vertex is the highest or lowest point on the parabola, represented as (h, k) in the vertex form.

Q: How is the focus of a parabola determined?

A: The focus is determined by adding the distance ‘p’ to the ‘k’ coordinate for vertical parabolas or to the ‘h’ coordinate for horizontal parabolas.

Q: Can the parabola open in any direction?

A: Yes, the direction depends on whether the parabola is vertical or horizontal.

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