Find the center and the radius of the circle x^2+y^2 -8x+14y= 12

We have the equation of the circle
:

x^2 + y^2 - 8x +14y = 12

We
will rewrite into the standard form: ( x-a)^2 + (y-b)^2 = r^2 such that (a,b) is the
center and r is the radius.

==> We will rewrite by
completing the square.

==> x^2 - 8x + 16 -16 + y^2 +
14y + 49 - 49 = 12

==> (x-4)^2 + (y+7)^2 = 12 + 49 +
16.

==> (x-4)^2 + (y+7)^2 =
77

Then the center of the circle is (4,-7)
and the radius is sqrt77.