This thread was useful for me since I was trying to figure the same question on.
More specifically, I wanted to know how the minor axis of the projected ellipse varies with tilting angle Phi.
I'll take a look at the Wikipedia website here referenced to see whether the equations there are of any use (If not, I'll have to figure out the relationship myself).
I'm intuitively guessing that if (x^2)/a^2 + (y^2)/b^2=1, all you have to do is divide by cos(phi) which ever axis is reduced upon tilting, if tilting parallel to either of the ellipse axes that is.
For example, if the ellipse is ORIGINALLY A CIRCLE on a plane P, it's shape is:
(x^2)/R^2 + (y^2)/R^2=1
If tilting parallel to the y axis, then the circle will start becoming an ellipse by reducing its radius along the x direction:
(x^2)/(R*cos[phi])^2 + (y^2)/R^2=1
Which is the same as:
(x^2)/a^2 + (y^2)/b^2=1
After the following variable substitution: