we know that
the equation of the sphere is equal to
[tex](x-h)^{2} +(y-k)^{2} +(z-l)^{2} =r^{2}[/tex]
where
(h,k,l) is the center of the sphere
r is the radius of the sphere
In this problem
the center is (5, 6, 1) and the radius is 2 units
so
the equation of the sphere is equal to
[tex](x-5)^{2} +(y-6)^{2} +(z-1)^{2} =2^{2}[/tex]
a) the equation of a circle that is parallel to the xy-plane is
For z=1
[tex](x-5)^{2} +(y-6)^{2} =2^{2}[/tex]
b) the equation of a circle that is parallel to the yz-plane is
For x=5
[tex](y-6)^{2} +(z-1)^{2} =2^{2}[/tex]
c) b) the equation of a circle that is parallel to the xz-plane is
For y=6
[tex](x-5)^{2} +(z-1)^{2} =2^{2}[/tex]
