On the Intersection of a Hyperboloid and a Plane

The intersection topic is quite popular at an interdisciplinary level. It can be the friends of geometry, geodesy and others. The curves of intersection resulting in this case are not only ellipses but rather all types of conics: ellipses, hyperbolas and parabolas. In text books of mathematics usually only cases are treated, where the planes of intersection are parallel to the coordinate planes. Here the general case is illustrated with intersecting planes which are not necessarily parallel to the coordinate planes. We have developed an algorithm for intersection of a hyperboloid and a plane with a closed form solution. To do this, we rotate the hyperboloid and the plane until inclined plane moves parallel to the XY plane. In this situation, the intersection ellipse and its projection will be the same. This study aims to show how to obtain the center, the semi-axis and orientation of the intersection curve.