Let C be a curve in R 2 given by an equation of the form f (x, y) = 0...

Let C be a curve in R ² given by an equation of the form f (x, y) = 0. The normal line to C at a point (x0, y0) on it is the line that passes through (x0, y0) and is perpendicular to C (meaning that it is perpendicular to the tangent line to C at (x0, y0)). In Exercises 31–33, find the normal lines to the given curves at the indicated points. Give both a set of parametric equations for the lines and an equation in the form Ax + By = C. (Hint: Use gradients.)