﻿ What makes a shape an ellipse? Visual animation to show this shape is created

# What makes an ellipse?

Conceptual understanding of what makes a shape an ellipse

#### What makes an ellipse ?

An ellipse is based around 2 different points. These 2 points are fixed and never move. In the demonstration below, we use blue tacks to represent these special points. Mathematicians have a name for these 2 points. We call each one a focus of the ellipse (link) .

Now that we have these two points, we are going to need a constant. This constant will obviously never change, and in the diagrams below the constant is represented by how long the yarn is. For instance, the yarn in diagrams 1 and 2 below has the constant length of 10.

Diagram 1
Diagram 2

The ellipse itself is a new set of points.

To create this set of points and to make our ellipse, the following statement must be true: the sum of the distances from anywhere on the ellipse to those 2 points ( blue tacks ) must be that constant number . This may sound like a lot of mathematical mumbo-jumbo. It's easier to understand this by looking at Diagrams 3- 7 .

Diagram 3 : Full Animation

That last sentence simply means that we draw an ellipse by adding up the 2 parts of the yarn to get the whole length of the yarn. The length of the yarn is constant and does not change.

Diagram 4
Diagram 5
Diagram 6
Diagram 7

Diagram 8
Diagram 9
Diagram 10
Diagram 11