Find the radius of the circle x^2 + y^2 +4x - 6y= 12

to find the radius, we will write the equation in the
standard form:

We know
that:

(x+a)^2 + (y-a)^2 = r^2    where (a,b) is the cente
and r is the radius:

==> x^2 + y^2 +4x - 6y =
12

Let us rewrite:

==: x^2 +
4x + y^2 - 4y = 12

Let us complete the
squares:

==> (x+2)^2 -4  + (y-3)^2 -9 =
12

==> (x+2)^2 + (y-2)^2 = 12 +
13

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

==> r^2 =
25

==> r=
5