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Proof of x and y int of a line

  1. Dec 11, 2009 #1
    1. The problem statement, all variables and given/known data
    prove that [tex]\sqrt{x}[/tex] + [tex]\sqrt{y}[/tex] = c
    Show that the sum of the x and y intercepts of any tangents to the line above = c (some positive constant).

    2. Relevant equations
    y1 - y2 = m(x1 - x2)
    dy/dx(for this problem) = -[tex]\sqrt{y}[/tex]/[tex]\sqrt{x}[/tex]

    3. The attempt at a solution
    So I get the slope, as written above, and put it into a point/slope equation, but where from here? When I try to solve for y = 0 and x = 0 I always have y2 and x2 left, I think I might just be doing something completely wrong, I haven't done something like this for a while. Is this even the right direction? Solve for the y and x int by making the opposite 0 in the equation, and then try to get the results, (the two interecepts) to add up to be [tex]\sqrt{x}[/tex] + [tex]\sqrt{y}[/tex]
  2. jcsd
  3. Dec 11, 2009 #2


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    Science Advisor

    First problem, I don't know what "x1", "y1", "x2", and "y2" are since you don't say. You mean, I think, that the equation of the tangent line at [itex](x_1, y_1)[/itex] is [itex]y- y_1= m(x- x_1).

    But your real problem is that the derivative of y with respect to x is NOT [itex]-\sqrt{y}/\sqrt{x}[/itex]. You have x and y reversed.
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