This is the maths representation of a problem which I have from the practice.
We have an interested cone with a diameter of the base $d$, height $h$ and the angle $\alpha$ as shown on the drawing. A plane $\gamma$ has been created which passes through the edge of the cone $A$ and again through the cone at point $B$ and the angle towards the base is $\beta$. Generally, the result section between the plane and the cone should be ellipse. The question is - is there any combination of values of $d, h, \alpha$ so that the section is circle?
A drawing of the problem can be found here:
I can't see your picture, but the intersection of a plane and cone will be a circle only if the plane is perpendicular to the axis of the cone.