how to find volume of the ellipse not in the origin by using the eigenvalues
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dear all,
i have matrix A has the information of an ellipse not in the origin. i need to find the volume of the ellipse using the eigenvalues but i got wrong volume. in 2-dimension i have points x enclosed by the ellipse that its information is A and b.
x = [ 0.55 0.0 ;
0.25 0.35
-0.2 0.2
-0.25 -0.1
-0.0 -0.3
0.4 -0.2 ]';
A=[ 2.4282 -0.0557
-0.0557 2.9680];
b=[-0.3393; -0.0562];
ei=eig(A)
vol=pi*sqrt(ei(1))*sqrt(ei(2));
the eigenvalues are ei=[ 2.4225, 2.9737 ]; the volume is 8.4320 which i think is wrong. can anyone help me to move the ellipse to the center to find the eigenvalues then the volume please. i tried to do that but its not correct.
many thanks,
Nadia,
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