Solve the equation in Problem 19 with the aid of the quadratic formula. Problem 19: T...

Solve the equation in Problem 19 with the aid of the quadratic formula.

Problem 19:

The differential equation

Where x = x(y), occurs in the study of optics. The equation describes the type of plane curve that will reflect all incoming light rays to the same point (see Problem 15, Exercises 1.2). Show that the curve must be a parabola. [Hint: Use the substitution and then re-examine Section 2.6.]