Find extreme points of a rotated ellipse function on a given axis How to find the points where it is most extreme on the X and Y axis? For example lets say I have an equation that describes an ellipse that is rotated (x RadiusX Rx y RadiusX Ux) 2 (x RadiusY Ry y RadiusY Uy) 2 RadiusY 2 How can I find the points where it will be most extreme on each axis Please keep in mind the values for variables RadiusX, RadiusY, Rx, Ry, Ux, Uy are known. An example with values ((x 1 0.70711) (y 1 0.70711)) 2 ((x 1.414213 0.70711) (y 1.414213 0.70711)) 2 1.414213 1.414213