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Parametric Curves: Tangent Lines

  1. Jan 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Find equations of the tangents to the curve x=3t^2+1, y=2t^3+1 that pass through the point (4,3).

    3. The attempt at a solution

    I was able to find the equation y=x-1 as a tangent line through the point (4,3) for the part of the curve above the x-axis since (4,3) is on the curve.

    However, I do not know how to find the equation of the tangent for the part of the curve below the x-axis since I do not know what point on the curve the tangent passes through and therefore do not know the t value.

    Any help is appreciated, thanks
  2. jcsd
  3. Jan 30, 2007 #2


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    Write down the equation for the tangent line to the curve at general value of t. Now put in the condition (4,3) is on the line. You should get a couple of cubic equations. You already know t=1 is a solution. Is there another?
  4. Jan 31, 2007 #3


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    Well, you get a cubic equation. Knowing that t= 1 is a solution makes it easy to solve. Dick's suggestion is right on the money.
  5. Jan 31, 2007 #4


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    Duh, right. Make that 'one' cubic.
  6. Jan 31, 2007 #5
    thanks a lot for the help, i was able to find the second equation, thanks
  7. Mar 7, 2009 #6
    So what *is* that second equation? I'm stuck!
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