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**

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