what are the coordinates for the center of the circle in the length of the radius X squared plus Y squared minus X minus 2Y -11 over four equals zero

Given:

The equation of a circle is:

To find:

The center of the circle and its radius.

Solution:

The standard form of a circle is:

         ...(i)

Where, (h,k) is center and r is the radius of the circle.

The given equation of the circle is:

Write the given equation in standard form of a circle.

On further simplification, we get

           ...(ii)

On comparing (i) and (ii), we get

Therefore, the center of the circle is (0.5,1) and radius is 2 units.