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Find Parabola With Focus and Directrix Calculator Online

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.

General Terms Table

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

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.

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.