Chapter 13.7, Problem 36ES

Use the result in Exercise 35 to show that the normal lines to the cones $z=\sqrt{x^2+y^2}\text{and}z=-\sqrt{x^2+y^2}$ are perpendicular to the normal lines to the sphere $x^2+y^2+z^2=a^2$ at every point of intersection (see Figure Ex-38).