Find the equation of the circle whose center (0,13) and the area = 25pi.

We'll write the equation of the circle in standard
form:

(x-h)^2 + (y-k)^2 = r^2, where h and k are the
coordinates of the center of the circle.

We'll identify h
and k:

h = 0 and k = 13

Now,
we'll determine the radius of the circle, using the formula for area of the
circle:

A = pi*r^2

25*pi =
pi*r^2

We'll divide by pi:

r^2
= 25

r = 5

We'll accept only
the positive value, since it is about a radius of a circle and it cannot be
negative.

Now,we'll substitute the coordinates of the
center of the circle and the value of radius in the equation of the
circle:

x^2 + (y - 13)^2 =
25

If we'll expand the square, we'll obtain
the general form of the equation:

x^2 + y^2 - 26y + 169 -
25 = 0

x^2 + y^2 - 26y  + 144 =
0