# SOLUTION: find the equation of the set of all points equidistant from the x axis and (4,0).

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 Click here to see ALL problems on Geometric formulas Question 62658: find the equation of the set of all points equidistant from the x axis and (4,0). Answer by jai_kos(139)   (Show Source): You can put this solution on YOUR website!Given a point (4 ,0) and Equation along the "x" axis, i.e. y = 0 Distance between a point (x ,y) and the point ( 4 ,0) is given by sqrt [ ( 0 -x) ^ 2 + ( 4 - y) ^2 ] = equal to the equation of line sqrt [ ( 0 -x) ^ 2 + ( 4 - y) ^2 ] = y Square on both sides of the baove equation, we get [x ^ 2 + ( 4 -y) ^2] = y ^ 2 Simplifying the above step we get, x^2 + 16 + y ^2 - 8y = y^2 x ^ 2 -8y + 16 = 0 The above equation represent the set of all points equidistant from x -axis and point ( 4, 0).