Focus and directrix construction of an ellipse

An ellipse is the set of points the same distance from a point S and a circle.[br]For the point P on the ellipse, segments SP and SQ have the same length, and the tangent line to the ellipse is the perpendicular bisector of SQ.[br]S is one focus of the ellipse, and the center of the circle, O, is the other focus.[br]The main claim to fame of Newton's calculus was a derivation of the motion of planets around the sun. Their orbits are elliptical, with the sun at one focus. The speed is not constant; in this diagram, the direction and size of the velocity are shown by the vector. Its length is the same as SI.[br][br](The velocity vector in this diagram is not exactly the real life one, but it’s close.)[br][br]About the diagram:[br][list][*]The slider makes point Q move around the circle, causing P to move around the ellipse. You can also use the animation button in the lower left.[br][/*][*]Some points can be dragged; try it. What changes?[br][/*][/list]