Parabola Equation Calculator

Find the equation of a parabola given its vertex and focus or directrix. Visualize the parabola and copy the equation.

Input Parameters

Vertex Coordinates (h, k)

Focus or Directrix

Focus Coordinates (x, y)

Directrix Equation (y = c or x = c)

Choose either Focus coordinates or Directrix equation.

Parabola Equation

$$$$

Visualization

Understanding Parabola Equations

A parabola is a symmetrical U-shaped curve. Every point on a parabola is equidistant from a fixed point (focus) and a fixed line (directrix). The vertex is the turning point of the parabola.

The standard equations for parabolas are:

Vertical Parabola: $ (x-h)^2 = 4p(y-k) $ (opens up if $p>0$, down if $p<0$)
Horizontal Parabola: $ (y-k)^2 = 4p(x-h) $ (opens right if $p>0$, left if $p<0$)

Here, $ (h, k) $ is the vertex, and $ p $ is the distance from the vertex to the focus and from the vertex to the directrix.

This calculator helps you determine the equation of a parabola by inputting the vertex and either the focus or the directrix. The visualization tool provides a graphical representation to enhance your understanding.

For further learning, visit: Math is Fun and Wikipedia.