If ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$is rotated 90° about origin, the equation of ellipse after rotation is:

The ellipse is centered at origin , if we assume that major axis is along the X-axis and minor axis is along Y-axis, upon rotating ${90}^0$ the major and minor axis gets interchanged .

Length of major axis becomes 2b and length of minor axis to 2a.

 So equation is $\frac{{\mathrm{x}}^2}{{\mathrm{b}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{a}}^2}=1$.