Student Tutorial: Equations of Parabolas

Instructions:

Learn how to find the equation of a parabola given the Focus and the Directrix. Study the examples and complete the Desmos graphing calculator activities.

Click the arrows on the bottom to get started

Math Clip Art: Student Tutorial Title Page

Equations of Parabolas

Geometrically, a parabola is the set of points equidistant from a point (the Focus) and a line (the Directrix). Focus Directrix

The Focus and Directrix are the same vertical distance from the vertex of the parabola.

With this parabola you can see that the distance from the focus to the point (2, 1) is the same as the distance from that point to the Directrix.

Now let’s look at a general point with coordinates (x, y).

The focus has coordinates (0, f). The point on the Directrix is (x, -f)

Use the distance formula to find D1 and D2.

Make the two distance formula expressions equal to each other to find the equation of the parabola.

Use this template to explore parabolas given the Focus and Directrix.

Now let’s look at an even more general case. The focus has coordinates (a, b) and the equation of the Directrix is y = c.

Once again, make the lengths of D1 and D2 equal to each other.

Given the coordinates (a, b) of the Focus and the equation y = c of the Directrix, you can find the equation of the parabola with this formula.

Use this template to explore parabolas given the Focus and Directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.

This math example shows how to derive the equation of a parabola given the focus and directrix.