# Technical Graphics - Plane Figures - The Ellipse

### What is an Ellipse ?

In the world today we are surrounded by Ellipses or partial Ellipses. From company logos to special engine parts Ellipses play an important part in our lives. Some bridges incorporate the Ellipse shape as it is a very strong structure. The planets revolve around the sun following elliptical paths. In this case the Sun is at one of the Foci of the Ellipse. (You will learn more about the Focal Points later.) You can see this to the right.

### The Ellipse and the Circle

You might not think it but the Ellipse and the Circle are very closly linked. A Circle is a special type of Ellipse, just like a Square is a special type of Rectangle, but the connection goes further than that. If you look at a circle obliquely, (that is not straight on), you will see an Ellipse. Take the picture of the satellite to the left. You know that the shape of a satellite when you look straight at it is a circle but you can see from the picture that when you look at it at a different angle you get an Ellipse. Now look at the picture of Big Ben in Londan to the right, you can see two clock faces and both of them look like Ellipses. Again this is because you are not looking at then straight on. If you still don't believe us, put your mouse oven the red circle below. This will cause the circle to rotate, therefore changing the angle at which you are looking at the Circle. Have a look and see what happens...

### The Ellipse and the Cone

The Ellipse like the Parabola, the Circle and the Hyperbola, is a Conic Section. This means that if a cone is cut in a certain way then you get one of the four curves mentioned above.

A cone cut by a simply inclined plane which cuts all of the cone's Generators results in an Ellipse. Below you can see a diagram.

If we take an Orthographic Projection of the cone, which has a simply inclined plane cutting it we can see from an auxillary plan of the cone the true shape of the resulting surface which turns out to be an Ellipse. You can see this below.

Earlier we said that an Ellipse and a Circle were closly linked. A Circle can be generated or created if you cut a cone with a plane that is perpendicular to its axis and which cuts all of the cone's generators.

### The Ellipse and the Cylinder

Just as it is true that if you cut a cone in a certain way you will get an Ellipse, you can also cut a Cylinder to get an Ellipse. To the right you can see a Cylinder cut by a simply inclined plane and the result is an ellipse.