Question

what is the standard form of the equation of the circle with the center (1,2) and contains the point (1,0)?

Answer 1

since the center is \((1,2)\) you know it looks like
\[(x-1)^2+(y-2)^2=r^2\] to find \(r^2\) find the square of the distance between \((1,2)\) and \((1,0)\)
the distance is pretty clearly \(2\) since they have the same \(x\) coordinate and the \(y\) coordinates are two apart

Answer 2

so the radius is 1 since the distance is the same as the diameter and half of the diameter would be 1?

Answer 3

no the radius is 2, and so the square of the radius is 4