The equation of a sphere with center (a, b, c) and radius r is given by :
[tex] (x-a)^{2} + (y-b)^{2} + (z-c)^{2} = r^{2} [/tex],
so the equation of the sphere with center (-3, 2, 9) and radius 6 is :
[tex](x-(-3))^{2} + (y-2)^{2} + (z-9)^{2} = 6^{2} [/tex]
[tex](x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]
The yz plane is the set of all points (0, y, z), that is x is always 0.
For x=0, the plane
[tex](x+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]
becomes
[tex](0+3)^{2} + (y-2)^{2} + (z-9)^{2} = 36[/tex]
[tex](y-2)^{2} + (z-9)^{2}=36-9=25= 5^{2} [/tex]
[tex](y-2)^{2} + (z-9)^{2}=5^{2} [/tex]
This is the circle with center (y, z)=(2, 9) and radius 5.
