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find all points on the hyperbola y=1/x, that are closest to the origin on (1/2,2)

  • math -

    Let P(x,y) be the closest point
    then if D is the distance, then
    D^2 = x^2 + y^2
    = x^2 + 1/x^2
    2D dD/dx = 2x - 2/x^3
    = 0 for a min of D
    2x = 2/x^3
    x^4 = 1
    x = ± 1

    if x=1, then y = 1
    if x = -1, then y = -1

    The two points closest to the origin are (1,1) and (-1,-1)

    Where does the (1/2,2) come in?
    Was that your answer?

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