What is the center and radius of the circle: x^2 + y^2 – 4x + 8y - 5 = 0. Also, what is the domain and range of the function?

The equation of the circle given is x^2 + y^2 – 4x + 8y -
5 = 0

x^2 + y^2 – 4x + 8y - 5 =
0

completing the squares

x^2 -
4x + 4 + y^2 + 8y + 16 = 5 + 4 + 16

=> (x - 2)^2 +
(y + 4)^2 = 5^2

This is in the standard form with center
(2, -4) and radius 5.

Consider a function that includes the
circle and the points that lie within it: (y + 4)^2 = 5^2 - (x -
2)^2

The domain of the function is all the values that x
can take for y to have a real value. The domain is the set of values [-3,
7]

The range of the function is the values that y takes for
values of x lying in the domain. The range is the set of values [-9,
1]