Expand the brackets:
x^2-3x+y^2+y=17.5
This is the equation of an ellipse which has the general form (x-h)^2/a^2+(y-k)^2/b^2=1. If it happens that a=b, the ellipse is a circle: (x-h)^2+(y-k)^2=a^2 where a is the radius and (h,k) are the coordinates of its centre.
We have to complete the squares:
x^2-3x+9/4+y^2+y+1/4 and then add the same constants to 17.5: 17.5+9/4+1/4=17.5+2.5=20.
This gives us (x-3/2)^2+(y+1/2)^2=20. So we have a circle with a^2=20 or a (the radius) = 2√5.
The centre of the circle is (3/2,-1/2) or (1.5,-0.5). I assume this is (a,b) in the question.