Question

Find the equations of two different circles so that each circle satisfies the conditions if the center is on the x-axis and graph is tangent to the horizontal line through the point (0,3)

Answer 1

equation of a circle with radius\(r\) and center \((h,k)\) is
\[(x-h)^2+(y-k)^2=r^2\]

Answer 2

radius is evidently 3 so you have
\[(x-h)^2+(y-k)^2=9\]
since the center is on the \(x\) axis, the \(y\) coordinate of the center is \(0\) so it is going to look like
\[(x-h)^2+y^2=9\]
to make up two examples, pick a couple different values for \(h\)