we know that
the equation of the sphere is equal to

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

<u>a) the equation of a circle that is parallel to the xy-plane is</u>
For z=1

<u>b) the equation of a circle that is parallel to the yz-plane is</u>
For x=5

<u>c) b) the equation of a circle that is parallel to the xz-plane is</u>
For y=6
