The applet lets you review constructions for parabolas and hyperbolas.
The center of the conic can be moved by dragging.
The major axis is parallel to the x-axis. The distance from the center to a vertex on the major axis and from the center to a focus are controlled by sliders.
The point on the conic can be moved by dragging.

An ellipse is the set of points for which the sum of the distances from the foci is a fixed constant.
A hyperbola is the set of points for which the difference of the distances from the foci is a fixed constant.