Question 1167224
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The center has coordinates


    x = {{{(4+8)/2}}} = 6    (the average of x-coordinates of endpoints).


    y = {{{(5+7)/2}}} = 6    (the average of y-coordinates of endpoints).


The radius is the distance from the center to either of endpoints


    r = {{{(6-4)^2 + (6-5)^2)}}} = {{{sqrt(2^2 + 1^2)}}} = {{{sqrt(5)}}}.


The equation of the circle in the standard form is


    {{{(x-6)^2}}} + {{{y-6)^2}}} = 5.      <U>ANSWER</U>
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Solved.