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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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.
can yu please explain me spectral theorem and corresponding eigen value
Originally Posted by prasum can yu please explain me spectral theorem and corresponding eigen value First of all: Did you cover it?. There are another methods for this problem. Regards.
no can yu suggest me some other method
Originally Posted by prasum no can yu suggest me some other method The equations of any rotation are: Substitute in the ellipse's original equation and make , you will obtain and you can fiind the canonical equation: Regards.
thanks
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