Suppose I have an ellipse with known semi-axis lengths. Its center point is in the origin and it is rotated about the x axis in some known angle .

I want to "stretch" this ellipse in the direction of some other angle .

By stretching I mean:

1) Rotating the system by gamma.

2) Multiplying the new Y dependent variable (in the new coordinate system) by some constant.

3) Rotating the system backwards by gamma.

I believe the resulting shape should still be an origin centered ellipse, with new semi-axis lengths and a new rotation angle about the x-axis. So far I've failed to prove it. Anyone have an idea?