Find the center of a circle whose diameter has endpoints points (-1,-5) and (5,-1) please help!!!

First:  Find the center of the circle; it will be half-ways between the two endpoints.

          To find the values of x and y, average them:  x  =  (-1 + 5)/2  =  4/2  =  2

                                                                                 y  =  (-5 + -1)/2  =  -6/2  =  -3

           The center of the circle is at (2, -3)

 

Second:  To find the radius, find the distance from the center to either endpoint (use the distance formula):

                d  =  sqrt( (-1 - 2)² + (-5 - -3)² )  =  sqrt( 9 + 4 )  =  sqrt(13)

 

Finally, place these into the formula for a circle:  (x - 2)² + (y - -3)²  =  ( sqrt(13) )²

                                                                             (x - 2)² + (y + 3)²  =  13