This document discusses finding the maximal deflection between the radial and normal directions on an ellipse. It defines the problem as locating the largest angle between the radial and normal vectors on the ellipse in the first quadrant. Using Lagrange multipliers, the document derives that the maximal deflection occurs at the point where the ellipse meets the line from the origin to the point (a,b), where a and b are the semi-major and semi-minor axes of the ellipse. The document also notes that this problem has applications to defining latitude on an ellipsoidal model of the Earth.