Find the center and radius of the circle whose equation is given by: x^2 + y^2 + 6x - 10 y = 9

x^2 + y^2 + 6x -10y = 9

To
find the radius and the center we need to rewrite the equation into the standard
form.

==> (x-a)^2 + (y-b)^2 = r^2 such
that the center is (a,b) and the radius is r.

We will
complete the square for x^2 and y^2.

==> x^2 + 6x +
y^2 -10y = 9

==> (x^2 + 6x +9)-9 + (y^2 -10y +25)
-25 = 9

==> (x+3)^2 + (y-5)^2 =
18+25

==> (x+3)^2 + (y-5)^2 =
43

==> Center = (-3,5) and
radius = sqrt43.