Chapter 8, Problem 19P

Consider the parabola:

x = 2(y-2)2 +3,and the point P(3,4).

(a) Write a polynomial expression for the distance d from point P to an arbitrary point Q on the parabola.

(b) Make a plot of d versus y for $0\le y\le 4$ .

(c) Determine the coordinates of Q if d = 3 (there are two points).

(d) Determine the coordinates of Q that correspond to the smallest d, and calculate the corresponding value of d.

(e) Make a plot that shows the parabola, point P, the two points from part (c), and the point from part (d).