what is the radius of a circle with center (1,-2) that passes through (1,0)?

the radius of the circle r (r>0) is equal to the distance between the center (1,-2) and (1,0):

r = ((1-1)^2 + (-2 - 0)^2)^0.5 = 4^0.5

r = 2 is the radius of the circle

what is the equation in standard form of the circle?

the equation in standard form of a circle with center (a,b)and radius r is:

(x-a)^2 + (y-b)^2 = r^2

in our case the center is (1, -2) that is a = 1 and b = -2 while the radius r = 2 thus the equation is

(x - 1)^2 + (y - (-2))^2 = 2^2

(x - 1)^2 + (y + 2)^2 = 4