Question

Find the equations that describe the circle of radius 2 centered at (4, 7, 6) that is parallel to the xy-plane. (Enter your answers as a comma-separated list of equations.)

Answer 1

Answer:

$(x-4)^2+(y-7)^2=4$

z=6

Step-by-step explanation:

The equation of a circle is satisfied by every point on it. The equation of a circle of radius r and point (h,k,l) parallel to the xy-plane is:

$(x-h)^2+(y-k)^2=r^2$

we can just substitute values into the equation:

$(x-4)^2+(y-7)^2=r^2$ where z=6

The radius is 2. Therefore:

$(x-4)^2+(y-7)^2=4$