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how to create an ellipse

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
how to create an ellipse

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.

Constant Length

Diagram 4
ellpse constant length demo
Diagram 5
ellpse constant length demo
Diagram 6
ellpse constant length demo
Diagram 7
ellpse constant length demo

Color Coded Diagrams

Diagram 8
color coded example of constant length from foci
Diagram 9
color coded example of constant length from foci
Diagram 10
color coded example of constant length from foci
Diagram 11
color coded example of constant length from foci

Back to Conic Sections Next to Focus of Ellipse