# Ellipse with a string

- Author:
- Marina Gitlin, Audrey McLaren

- Topic:
- Ellipse

Follow the steps! Imagine that the point D is a pencil tip that is pulling tightly on a string, and that string is represented by the two lines L1 and L2.

Follow the instruction on the screen. What happens to the ellipse as the foci move closer together? Compare and ellipse where the foci are far apart and foci that are close together. What happens when both foci move into the origin?

Let the length of major radius be *a* and the length of the minor radius be *b*. What is the length of the string as it relates to *a*, and/or *b? *

Let the focal radius (the distance between the center and a focus) be *c. *Place the point D on the y-axis and consider the resulting picture.
State the relationship between *a, b, and c *(the major radius, minor radius, and focal radius)