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Find the equation of the circle

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Center (0,0) and passing through (1/4, √31/4) The endpoints is a diameter are (7,3) and (-1,-3)

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Diameter = √((7--1)^2 +(3--3)^2) = √(64+36) = √100 = 10 (x -0)^2 + (y-0)^2 = (10/2)^2 x^2 + y^2 = 25

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As Randy points out, the data you gave is inconsistent. You gave (0, 0) as the center, but the center would also be the midpoint of a diameter, which would be (7-1 / 2, 3-3 / 2) = (3, 0).

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this must be 2 separate problems 1. Center (0, 0) and passing through (1/4, √31/4) r = sqrt( 1/16 + 3/16) = 1/2 x^2 + y^2 = 1/4 <<< answer 2. The endpoints is a diameter are (7, 3) and (-1, -3) d = sqrt( 8^2 + 6^2) = 10 ... radius = 5 (7 + -1) / 2 = 3 = h (3 + -3) / 2 = 0 = k (x - 3)^2 + (y - 0)^2 = 25

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No such circle exists!

            
        

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