I need to find the area of the circle with equation x^2+y^2-6x+4y=36.

We'll recall the formula for the area of the
circle:

A = pi*r^2

In order to
evaluate the area of the given circle, we need to compute it's
radius.

For this reason, we'll re-write the general
equation of the circle in standard form:

(x - h)^2 + (y -
k)^2 = r^2

(h,k) are the coordinates of the center of the
circle and r is the radius of the circle.

We'll use the
technique of completing the square:

(x^2 - 6x + 9) + (y^2 +
4y + 4) - 9 - 4 = 36

(x - 3)^2 + (y + 2)^2 = 36 +
13

(x - 3)^2 + (y + 2)^2 =
49

The coordinates of the center are (3,-2) and the radius
is r = sqrt49 = 7

The requested area of the
circle is: A = 49*pi square units.