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

**Vertical Parabola:**- Vertex form: (
*x*−*h*)^{2}=4*p*(*y*−*k*) - Focus: (
*h*,*k*+*p*) - Directrix:
*y*=*k*−*p*

- Vertex form: (
**Horizontal Parabola:**- Vertex form: (
*y*−*k*)^{2}=4*p*(*x*−*h*) - Focus: (
*h*+*p*,*k*) - Directrix:
*x*=*h*−*p*

- Vertex form: (

**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:

Term | Meaning |
---|---|

Vertex | The point (h, k) on the parabola. |

Focus | The focal point of the parabola. |

Directrix | The line that is equidistant from all points on the parabola. |

Parabola | A 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.

## 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.