Parabola as a Locus of Centers of Circles

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

A parabola is the set of all the points that are equidistant from a fixed point (the focus, red point) and a fixed line (the directrix, dashed green line).

[more]

Given a circle and a line (in any position relative to ), the locus of the centers of all the circles that are tangent to both and is a parabola (dashed red curve) whose focal point is the center of .

[less]

Contributed by: Abraham Gadalla (June 2012)
Open content licensed under CC BY-NC-SA


Snapshots


Details

In this Demonstration, is the origin .

Let be the distance from to and be the radius of . If is vertical, then the equation of the parabola is , where is the focal distance .



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send