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show that the equation of the curve intersecting with the x axis at the point x = 1 and for which the length of the subnormal at any point of the curve is equal to the arithmetic mean of the coordinates of this point is (y – x)^2(x + 2y) = 1 GN BERMAN PROBLEM please help

show that the equation of the curve intersecting with the x axis at the point x = 1 and for which the length of the subnormal at any point of the curve is equal to the arithmetic mean of the coordinates of this point is (y – x)^2(x + 2y) = 1 GN BERMAN PROBLEM please help

Grade:12

1 Answers

Sumit Ghosh
24 Points
7 years ago
I think there is some mistake with the question .Curve passes through (1,0),as it intersects x axis at x=1.Length of subnormal = yy`.According to the ques. yy`= (1+0)/2=1/2ydy=dx/2y^2/2=x/2+ kY^2 = x+cIt passes through (1,0)c=-1 hence y^2=x-1

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