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Homework Help: Points that a curve's normal line intersects

  1. Jun 28, 2012 #1
    1. The problem statement, all variables and given/known data

    The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point?

    2. The attempt at a solution

    I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal line. I'm not really sure where to approach from here... any hints?
  2. jcsd
  3. Jun 28, 2012 #2


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    Have you noticed that ##x^2+2xy-3y^2\ ##factors? What does its graph look like? Finding where that normal line hits it again won't seem so difficult.
  4. Jun 29, 2012 #3
    D'oh! I was looking way too hard. I can't believe I missed that.

    Thanks for you time! I greatly appreciate it.
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