We have that the coordinates given are for a sphere.
As we look for a circle parallel to the xy plane, then our xy coordinates are:
(x, y) = (4, 2)
The standard equation of the circle is:
(x - h) ^ 2 + (y - k) ^ 2 = r ^ 2
where h and k are the x and y coordinates of the center of the circle and r is the radius.
We have then:
h = 4
k = 2
r = 3
The equation of the circumference is:
(x - 4) ^ 2 + (y - 2) ^ 2 = 9
answer
(x - 4) ^ 2 + (y - 2) ^ 2 = 9
