Write the circle equation if it passes through the point (5,4) and the center of circle is (2,0).

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 =
0.

We'll substitute them into the
equation:

(x - 2)^2 + (y - 0)^2 =
r^2

 We'll determine the radius considering the constraint
from enunciation that the circle is passing through the point
(5,4).

If the circle is passing through the point (5,4),
then the coordinates of the point are verifying the equation of the
circle:

(5 - 2)^2 + (4 - 0)^2 =
r^2

3^2 + 4^2 = r^2

9 + 16 =
r^2

25 = r^2

r =
5

Note: we remark that 3,4 are the pythagorean numbers, so
the radius could only be 5.

The equation of
the circle is:

(x - 2)^2 +
(y)^2 = 25