Question

Find the equations that describe the circle of radius 2 centered at(5, 6, 1)that is parallel to the xy-plane. (enter your answers as a comma-separated list of equations.)

Answer 1

we know that

the equation of the sphere is equal to

$(x-h)^{2} +(y-k)^{2} +(z-l)^{2} =r^{2}$

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

$(x-5)^{2} +(y-6)^{2} +(z-1)^{2} =2^{2}$

a) the equation of a circle that is parallel to the xy-plane is

For z=1

$(x-5)^{2} +(y-6)^{2} =2^{2}$

b) the equation of a circle that is parallel to the yz-plane is

For x=5

$(y-6)^{2} +(z-1)^{2} =2^{2}$

c) b) the equation of a circle that is parallel to the xz-plane is

For y=6

$(x-5)^{2} +(z-1)^{2} =2^{2}$