How to predict the shape of the circle from any point of view?

[OFF_Smog]

As we know a circle view at an angle appears as an ellipse,
as you see in the picture, the center of the camera aim to the center of the circle ,
the angle between the circle axis and the camera is ө,
the azimuth between mojor axis(a) and the camera is ∞,
the rotation of the camera is €,

1. How to predict an orientation of major and minor axis and the ratio of its axes(b/a)?? ,if we only know these ө,∞,€ angle, regardless of size of ellipses.

2. Is there any theory to apply this example?

 

[fresh_42]

Not sure what there is to predict. In general what the camera does is a projection of the circle, or if we consider cone cuts, the variation of the camera. So one could calculate the position of the camera with respect to a fixed cone.