What is the area of the circle whose equation is x^2 + y^2 - 2x + 4y = 32

Given the equation of the circle
is:

x^2 + y^2 -2x + 4y = 32

We
need to find the area of the circle.

To find the area, we
need to determine the radius of the circle (r).

We can
determine r by rewriting the circle equation into the standard
form.

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

Let us rewrite by completing the
square.

==> x^2 + y^2 - 2x + 4y =
32

==> x^2 - 2x + y^2 + 4y =
32

==> x^2 - 2x + 1 -1 + y^2 + 4y + 4 - 4 =
32

==> (x-1)^2 -1 + ( y+2)^2 - 4 =
32

==> (x-1)^2 + (y+2)^2 = 32 +
5

==> (x-1)^2 + (y+2)^2 =
37

Then, we conclude that r^2 =
37.

==> r=
sqrt(37).

Now we will determine the
area.

==> The area (a )= r^2 * pi =
37*pi = 116.24 square units (approx.)