Given the circle center (1,1) and the point on the circle (3,5) what is the equation of the circle.

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 = 1 and k =
1.

We'll substitute them into the
equation:

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

 We'll determine the radius considering the constraint
from enunciation that the circle is passing through the point
(3,5).

If the circle is passing through the point (3,5),
then the coordinates of the point are verifying the equation of the
circle:

(3 - 1)^2 + (5 - 1)^2 =
r^2

2^2 + 4^2 = r^2

4 + 16 =
r^2

20 = r^2

r =
2sqrt5

Note: we'll reject th negative value of radius
-2sqrt5.

The equation of the circle
is:

(x - 1)^2 + (y - 1)^2 =
20