your equation is:
(x-(-0.5))^2+(y-4)=2.5^2?
that is actually the equation of a parabola, as shown below.
it would be the equation of a circle if you squared the y term to get:
(x-(-0.5))^2+(y-4)^2=2.5^2
simplify a litle to get:
(x + .5)^2 + (y-4)^2 = 2.5^2
it is now in what is called the standard form of the equation of a circle.
that would look like this:
the standard form of a circle equation is:
(x - h)^2 + (y-k)^2 = r^2
the center is at (h,k).
the radius is r.
(h,k) for your equation is (-.5,4)
r for your equation is 2.5
that would look like this:
if you simplify the original equation (after i squared the y term), you would do the following:
start with:
(x-(-0.5))^2+(y-4)^2=2.5^2
since - -.5 is equal to + .5, you would get:
(x + .5)^2 + (y-4)^2 = 2.5^2
you would perform the operations indicated to get:
x^2 + x + .25 + y^2 - 8y + 16 = 6.25
subtract 6.25 from both sides of the equation to get:
x^2 + x + .25 + y^2 - 8y + 16 - 6.25 = 0
combine like terms to get:
x^2 + x + y^2 - 8y + 10 = 0
it is now what is called the general form.
here's a reference.
https://www.mathsisfun.com/algebra/circle-equations.html