What is the area of the circle x^2 + y^2 - 6x +12 y= 20?

Given the equation of the circle
:

x^2 + y^2 - 6x + 12y =
20

First we will rewrite the equation into the standard
form

(x-a)^2 + (y-b)^2 = r^2 such that r is the
radius.

We will complete the square for x^2 -6x and y^2
+12y

==> x^2 - 6x + 9 -9 + y^2 + 12y +36 - 36 =
20

==> (x-3)^2 + (y+6)^2 = 20 + 9 +
36

==> (x-3)^2 + (y+6)^2 =
65

Then the radius of the circle is
sqrt65.

Now we will calculate the
area.

==> A = r^2 * pi = sqrt65^2 * pi
65pi

Then the area of the circle is 65pi
square units.