Ellipse Area and Circumference

Date: 04/19/2001 at 20:34:07
From: Sonja Farthing
Subject: Ellipses

Hi, 

I need to find out how to find the area and circumference of an 
ellipse, as well as how to draw one for a school project. I have 
looked at some of the ones in the archives but do not understand the 
answers or the symbols. Please help me.

Thank you.

Date: 04/19/2001 at 21:26:20
From: Doctor Jaffee
Subject: Re: Ellipses

Hi Sonja,

You can draw two line segments through an ellipse, each of which will 
split the ellipse into two pieces that are reflections of each other. 

 
In other words, an ellipse has two axes of symmetry, one horizontal 
and the other vertical.

Now, if we call the distance from the center of the ellipse to an end 
of the horizontal axis of symmetry a, and we let b equal the distance 
from the center to the end of the vertical axis of symmetry, then the 
area of the ellipse will be pi*a*b, where pi is approximately 3.14.

   

We can find the circumference using calculus, but an easier method 
(although it only results in an approximate answer) is the formula 
circumference = 2*pi*sqrt[(1/2)(a^2 + b^2)].

Here is one way you can draw an ellipse. Get a piece of corkboard and 
attach a piece of paper (the longer side oriented left to right) to 
the corkboard using two thumbtacks, the first thumbtack approximately 
4 inches from the left of the center of the paper and the other 
thumbtack about 4 inches to the right of center. Attach a piece of 
string, one end to each thumbtack. The length of string should be 
about 10 inches. Pull the string taut with a pencil and, keeping the 
string taut, move your pencil along the paper. The result should be an 
ellipse.

I hope this explanation is helpful. If it needs clarification, write 
back, or if you are having difficulties, let me know.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/