Parabola Equation Calculator

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.