Least Squares approximation of an ellipse

[JellyFish]

I have tried looking for some stratgeies or techniques online to solve this problem but came out empty handed. We have done linear and parabola ones in class but I'm not quite sure how to do least squares approximation with an ellipse.

The ellipse is (X[sup:1gb2sjqp]2[/sup:1gb2sjqp]/a[sup:1gb2sjqp]2[/sup:1gb2sjqp]) + (y[sup:1gb2sjqp]2[/sup:1gb2sjqp]/b[sup:1gb2sjqp]2[/sup:1gb2sjqp]) = 1

The points are (-5, -2), (-2, -3.9), (1,4), (4,3), and (5,2).

With this I need to find the least squares approximation.

Thanks.

 

[galactus]

Did you google anything?.

Here is a site that pertains to it. I saw many more.

http://www.mathworks.com/matlabcentral/ ... edemo.html

and here:

http://www.emis.de/journals/BBMS/Bullet ... gander.pdf

I have never done this myself. Apparently it is tricky.