find the center and radius of the circle with equation: x^2+y^2+6x-4y-15=0

x^2 + y^2 + 6x - 4y - 15 = 0

First
we need to rewrite the equation using the standard form for the
circle:

( x-a)^2 + ( y-b)^2 = r^2    such
that:

(a,b) is the center and r is the
radius:

To rewrite the equation we need to complete the
square:

==> (x^2 + 6x) + (y^2 - 4y) =
15

==> (x^2 + 6x + 9 -9 ) + ( y^2 - 4y -4 + 4) =
15

==> (x + 3)^2 - 9 + ( y-2)^2  + 4 =
15

==> (x+3)^2 + (y-2)^2 = 15 - 4 +
9

==> (x+3)^2 + (y-2)^2 =
20

Then the center is ( -3, 2)  and r= sqrt20=
2sqrt5