Elliptical Cross Sections

Elliptic Conic Section

If the conic is an ellipse, 0<e<1. This implies

[math]e=\frac{\sin \beta}{\sin \alpha}=\frac{\sin\ (25^{\circ})}{\sin (90^{\circ}-\theta)}[/math]

[math]\frac{sin (25^{\circ})}{cos (\theta)}=e[/math]

since e must be less than 1, this sets the limit of theta at less than 65 degrees. Since the limit of [math]\theta=0[/math], this implies the minimum eccentricity will be [math]e\approx .4291[/math]

This implies that the shape made on the the plane of the sector is an ellipse for angles

[math] 0\lt \theta\lt 65^{\circ}[/math]