Normals to an Ellipse from any given Point

Abstract

Let a straight line MN of length a+b slide between two rectangular lines XOX', YOY', Let it be divided at P into parts MP = a, PN =b. The locus of P, we know, is an ellipse. In y, fact, if the angle MNO = Φ, the co-ordinates of P are a cosΦ, b sinΦ referred to OX, OY as axes, and P describes the ellipse x²/a²+y² b²=1 we shall call E.