Suppose $AB$ is a diameter of a circle and $P$ is a plane through $AB$ making angle $a$ with the plane of the circle.If diameter of the circle be $2A$,then the question is to find out the eccentricity of the curve of projection of the circle on $P$
I am aware of the fact that the projected area on a plane is the area of circle times $\cos$ of the angle between the circle and the plane.By this I could find out the projected area of the circle on the plane as $\pi A^2 \cos a $ Comparing this with the area of ellipse I assumed the semi minor axis as $A\cos a$ and semi major axis as $A$ which gives eccentricity as $\sin a$ but I am not sure if this approach is correct.Any ideas?Thanks.