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
