Ellipse

An ellipse is like a squashed circle.

 

Just like a Circle has one center, an ellipse has two "centers" called foci.

The distance f+g is always the same value

In other words, when you go from point "F" to any point on the ellipse and then go on to point "G", you will always travel the same distance.

 

You Can Draw It Yourself

Put two pins in a board, put a loop of string around them, and insert a pencil into the loop. Keep the string stretched so it forms a triangle, and draw a line ... you will draw an ellipse.

It works because the string naturally forces the same distance from pin-to-pencil-to-other-pin.

A Circle is an Ellipse In fact a Circle is an Ellipse, where both foci are at the same point (the center). In other words, a circle is a "special case" of an ellipse. Ellipses Rule!

Definition

 

Section of a Cone You can also get an ellipse when you slice through a cone (but not too steep a slice, or you get a parabola or hyperbola). In fact the ellipse is a conic section (a section of a cone) with an eccentricity between 0 and 1.

Calculations

Area The area of an ellipse is π × a × b (If it is a circle, then a and b are equal to the radius, and you get π × r × r = πr2, which is right!)

Perimeter Approximation

Rather strangely, the perimeter of an ellipse is very difficult to calculate, so I created a special page for the subject: read Perimeter of an Ellipse for more details.

But a simple approximation that is within about 5% of the true value (so long as a is not more than 3 times longer than b) is as follows:

Remember, this is only a rough approximation!

Equation By placing an ellipse on an x-y graph (with its major axis on the x-axis and minor axis on the y-axis), the equation of the curve is: x2/a2 + y2/b2 = 1 (very similar to the equation of the hyperbola: x2/a2 - y2/b2 = 1, except for a "+" instead of a "-")