Calculate the area of the circle if we are given that equation of the circle as x^2 +y^2 - 8x +12y = 12

Given the equation of the
circle:

x^2 + y^2 - 8x + 12y =
12

We need to rewrite the equation into the standard form
in order to determine the radius.

==> (x-a)^2 +
(y-b)^2 = r^2

Then we will need to complete the
square.

==> x^2 - 8x + 16 -16 + y^2 + 12y + 36 -36 =
12

==> (x-4)^2 + (y+6)^2 = 12 + 36 +
16

==. (x-4)^2 + 9y+6)^2 =
64

==> (x-4)^2 + (y+6)^2 =
8^2

Then the radius is r=
8.

Now we will calculate the
area.

==> A= r^2 * pi = 8^2 * pi = 64*pi =
201.06

Then the area of the circle is 64pi =
201.06 square units.