Using Calculus, find the point on circle $(x-3)^2+(y-1)^2=16$ that is closest to arbitrary point $(-2,2)$ in $x-y$ plane that is not on the circle.

Question

Problem

Using Calculus, find the point on the circle $(x-3)^2 + (y-1)^2 = 16$ that is closest to arbitrary point $(-2,2)$ in the $x-y$ plane that is not on the circle.

My Attempt : Attached images show the derivation from which I took the first derivative. I took the derivative of what I believed to be the distance formula from the point to a point on the circle. Please advise.

Answer 1

The line that passes through $(—2,—2)$ and the center of the circle intersects the circle at the closest and the farthest point.