Really have no idea as to how to proceed:

Find a point P on the graph of

x^(2)+y^(2)−62x-12y+828=0

and a point Q on the graph of

(y-6)^(2)=x^(3)−56x^(2)−90x+29988

such that the distance between them is as small as possible.

To solve this problem, we let (xy) be the coordinates of the point Q. Then we need to minimize the following function of x and y:

1)_____________________

After we eliminate y from the above, we reduce to minimizing the following function of x alone:

2) f(x)=______________

To find the minimum value of f(x) we need to check the value at the following three points (in increasing order). (You will need to use a numerical method, like Newton-Raphson to find one of these points.)

3) x1=___________

4) x2=___________

5) x3=___________

We conclude that the minimum value of f(x) occurs at

6) x=_____________

Thus a solution to our original question is

7) P=(____,____)

8) Q=(____,____)