SOLUTION: The endpoints of the diameter of the circle are (4,5) and (8,7). Find the equation of the circle in standard form

Algebra ->  Circles -> SOLUTION: The endpoints of the diameter of the circle are (4,5) and (8,7). Find the equation of the circle in standard form       Log On


   

Question 1167224: The endpoints of the diameter of the circle are (4,5) and (8,7). Find the equation of the circle in standard form
Answer by ikleyn(52846) About Me  (Show Source):
You can put this solution on YOUR website!
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The center has coordinates


    x = %284%2B8%29%2F2 = 6    (the average of x-coordinates of endpoints).


    y = %285%2B7%29%2F2 = 6    (the average of y-coordinates of endpoints).


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


    r = %286-4%29%5E2+%2B+%286-5%29%5E2%29 = sqrt%282%5E2+%2B+1%5E2%29 = sqrt%285%29.


The equation of the circle in the standard form is


    %28x-6%29%5E2 + y-6%29%5E2 = 5.      ANSWER


Solved.