The firsdt equation describes a parabola opening to the right.

The second equation describes a circle around C(6, 0) with .

Enlarge the circle around C until it touches the parabola. The difference between the larger radius and the original radius is the shortest distance between the parabola and the circle:

New circle with variable radius.

Point of intersection:

Solve for x:

There is only one point of intersection, that means the 2 curves are tangent, if

The shortest distance is therefore: