find the equation of the circle with the center (2,1) if the circle passes through (4,1)

We'll write the equation of the
circle:

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

The center of the circle has the coordinates C(h ;
k).

We know, from enunciation, that h = 2 and k =
1.

We'll substitute them into the
equation:

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

 We'll find the radius considering the condition from
enunciation,namely that the circle is passing through the point
(4,1).

If the circle is passing through the point (4,1),
then the coordinates of the point are verifying the equation of the
circle:

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

2^2 + 0^2 = r^2

r =
2

The equation of the circle
is:

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