Question

Find the point on the sphere x squaredplusleft parenthesis y minus 4 right parenthesis squaredplusleft parenthesis z minus 8 right parenthesis squaredequals9 nearest to
a. the​ xy-plane.
b. the point left parenthesis 0 comma 8 comma 8 right parenthesis.

Answer 1

The center of the sphere of radius 3 is (0, 4, 8).

a) The point nearest the plane z=0, will be (0, 4, 5), one radius length below the center toward the xy-plane.

b) The line between the sphere's center and the given point is (x, z) = (0, 8). As in part (a), the closest point on that line to the given point is one radius-length from center along that line, or (0, 7, 8).