Calc 3 Show that the equation is a sphere

1. Show that:

x^2+y^2+z^2+6x+8y-4z+4=0

is an equation of a sphere. Find the radius and the center of the sphere.

2. Find an inequality satisfied by all points that belong to the closed ball with radius 6 and center (0,-2,-3)

10 pts best answer. Thanks!

1. Complete the square(s) to put into standard form.
x^2 + y^2 + z^2 + 6x + 8y - 4z + 4 = 0
(x^2 + 6x + 9) - 9 + (y^2 + 8y + 16) - 16 + (z^2 - 4z + 4) = 0
(x + 3)^2 + (y + 4)^2 + (z - 2)^2 = 25
So the radius is 5 and the centre is C(-3, -4, 2).

2. The ball is closed, so:
x^2 + (y + 2)^2 + (z + 3)^2 ≤ 36

Put the equations into standard form by completing the square.