A conic section is the plane curve formed by the intersection of a plane and a right-circular, two-napped cone. Such a cone is shown here.

The cone is the surface formed by all the lines passing through a circle and a point. The point must lie on a line, called the "axis," which is perpendicular to the plane of the circle at the circle's center. The point is called the "vertex," and each line on the cone is called a "generatrix." The two parts of the cone lying on either side of the vertex are called "nappes." When the intersecting plane is perpendicular to the axis, the conic section is a circle.

When the intersecting plane is tilted and cuts completely across one of the nappes, the section is an oval called an ellipse.

When the intersecting plane is parallel to one of the generatrices, it...