What is the center and the radius of the circle x^2 + y^2 -3x + 5y -25 = 0

x^2 + y^2 -3x + 5y -25 = 0

We
are given the equation of the circle.

We need to determine
the radius and the center of the circle.

First, we need to
rewrite the equation into the standard form:

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

Then we will complete the
squares.

==> x^2 -3x + y^2 +5y =
25

=> x^2 -3x + 9/4 + y^2 + 5y + 25/4 = 25 + 9/4 +
25/4

==> (x -3/2)^2 + (y+5/2)^2 =
(100+9+25)/4

==> (x-3/2)^2 + (y+5/2)62 = 134/4 =
33.5

==> (x-3/2)^2 + (y+5/2)^2 =
33.5

Then, the center of the circle is the
point (3/2, -5/2)

and the
radius is sqrt(134) /2 = sqrt(33.5) = 5.79
(approx).