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Use implicit differentiation to find the points of tangency

  1. Nov 18, 2004 #1
    Please Help!!

    Ok, im having problem with an Implicit differentiation problem...
    Two tangent lines to the hyperbola [tex] 9x^2 - y^2 =36 [/tex] intersect at the y-axis.

    Use implicit differentiation to find the points of tangency. Ok so i implicitly differentiated this function and i came up with y'= 9x/y...now...Im not sure on how to find the points of tangency. Do i have to set the two equations equal to eachother and solve for y and x seperately? Please help, and help will be appreciated!! thanks
     
  2. jcsd
  3. Nov 19, 2004 #2

    HallsofIvy

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    You really don't need to worry about "two" tangent lines. Choose any point on the ellipse, find the tangent line and see where it intersects the y_axis.

    Let (x0, y0) be the point of tangency. Then the slope of the tangent line is, as you found, 9x0/y0 and the equation of the tangent line is [itex]y= \frac{9x_0}{y_0}(x- x_0)+ y_0[/itex]. At the y-axis, x= 0 so
    [itex]y= \frac{9x_0}{y_0}(-x_0)+ y_0= \frac{-9x_0^2+y_0^2}{y_0}[/itex].
     
  4. Nov 19, 2004 #3
    Thank you for your response! I was just confused on what to pick the points as. Thanks again
     
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