4. Show that x2 + y2 + z2 + 4x – 6y + 2z + 6 = 0 is the equation of a sphere. Also, find its center and radius.

Answer 1

x^2 + y^2 + z^2 + 4x - 6y + 2z + 6 = 0
x^2+4x + y^2-6y + z^2+2z = -6
x^2+4x+4 + y^2-6y+9 + z^2+2x+1 = -6+4+9+1
(x+2)^2 + (y-3)^2 + (z+1)^2 = 8
center at (-2,3,-1) and radius = √8

Answer 2

(-6,8/4,3) radius =8