Find the equations that describe the circle of radius 3 centered at (4, 2, 5) that is parallel to the xy-plane. (enter your answers as a comma-separated list of equations.)

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