The program is MATLAB

19. Consider the parabola: x = 2(y-2)2 + 3 , and the point P(3, 4). (a) Write a polynomial expres- 4 P(3,4) y 2 sion for the distance d from point P to an arbitrary point 0 on the parabola. 0 2 4 6 8 10 12 (b) Make a plot of d versus y for (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). 19. Consider the parabola: x = 2(y-2)2 + 3 , and the point P(3, 4). (a) Write a polynomial expres- 4 P(3,4) y 2 sion for the distance d from point P to an arbitrary point 0 on the parabola. 0 2 4 6 8 10 12 (b) Make a plot of d versus y for (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)