Normals to a parabola

Abstract

Given a parabola in the standard form corresponding to three points on the parabola, such that the normals at these three points concur at a point the equation of the circumscribing circle through the three points provides a tremendous opportunity to illustrate ‘The Art of Algebraic Manipulations’. The equation of the circle exists as a separate entity depending on the values of the parameters The graphical illustrations are based on Scientific WorkPlace 5.5 and they provide interesting interpretations of the roots of cubic equations. Geometry, algebra and the theory of cubic equations are amply illustrated in this article.