Find a point P on the graph of
x^2+y^2- 142 x - 10 y + 4841 = 0
and a point Q on the graph of
(y - 5)^2 = x^3 - 155 x^2 - 274 x + 583248
such that the distance between them is as small as possible.

To solve this problem, we let

After we eliminate

To find the minimum value of

We conclude that the minimum value of

Thus a solution to our original question is

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