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Show that the gradient of the curve

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that the gradient of the curve [tex]\frac{a}{x}+\frac{b}{y}=1[/tex] is [tex]-\frac{ay^2}{bx^2}[/tex]. The point (p,q) lies on both the straight line [itex]ax+by=1[/tex] and [tex]\frac{a}{x}+\frac{b}{y}=1[/tex] where ab =/= 0. Given that, at this point, the line and the curve have the same gradient, show that p=±q.


    3. The attempt at a solution

    [tex]\frac{a}{x}+\frac{b}{y}=1[/tex]

    [tex]\frac{dy}{dx}=-ax^{-2}-by^{-2}[/tex]

    [tex]-\frac{b}{y^2}\frac{dy}{dx}=\frac{a}{x^2}[/tex]

    [tex]\frac{dy}{dx}=-\frac{ay^2}{bx^2}[/tex]
    1. The problem statement, all variables and given/known data

    Not sure how to calculate the next part..



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 7, 2011 #2
    You already did the difficult part.

    Now find the gradient of the straight line and equate the two gradients.

    The put x = p and y = q.
     
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