if A represents the area of the ellipse 3(x^2)+4xy+3(y^2)=1 then the value of (3sqrt(5)/(pi))*A

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- Nov 16th 2010, 10:39 AMprasumellipse area
if A represents the area of the ellipse 3(x^2)+4xy+3(y^2)=1 then the value of (3sqrt(5)/(pi))*A

- Nov 16th 2010, 11:13 AMFernandoRevilla
The ellipse can be written:

By the Spectral Theorem, there is an orthogonal transformation (i.e. preserving distances) such that the ellipse's equation is:

where are the corresponding eigenvalues. In this case . So,

Then,

.

Regards. - Nov 16th 2010, 11:06 PMprasum
can yu please explain me spectral theorem and corresponding eigen value

- Nov 16th 2010, 11:35 PMFernandoRevilla
- Nov 16th 2010, 11:48 PMprasum
no can yu suggest me some other method

- Nov 17th 2010, 04:29 AMFernandoRevilla
- Nov 17th 2010, 05:59 AMprasum
thanks