Final answer:
To find the center and radius of the circle defined by the equation, rewrite the equation in standard form by completing the square. The center of the circle is (-1/4, 1) and the radius is √(25/8).
Step-by-step explanation:
To find the center and radius of a circle defined by the equation x^2+y^2+1/2x−2y−5=0, we need to rewrite the equation in standard form by completing the square.
The given equation can be rewritten as (x^2+1/2x) + (y^2-2y) = 5.
Completing the square for x and y, we get (x+1/4)^2 + (y-1)^2 = 25/8. This equation is in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Therefore, the center of the circle is (-1/4, 1) and the radius is √(25/8).