oblique ellipse equation

Описание: We generally know about the ellipse equation (X^2/a^2)+(Y^2/b^2)=1 where a and b are the semi-major and semi-minor axis lengths respectively. But what happens when these lines have some change or deviation from the axis. Suppose a is now a'=a cos (phi) where phi is the angle between the old and the new x-axis. Here we see many changes in the ellipse.
(X^2/a^2)+(Y^2/b^2)=2XY/(sqrt(2)*a*b)+ 0.5 is the new equation. A little deviation from the original.
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P.S.
This video is for educational purposes only. I would like to thank the DESMOS app creators for their wonderful online as well as offline mathematical tools in guiding us.