19. Consider the parabola:

, and the point

.

(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

.

(c) Determine the coordinates of Q if (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).