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Need help on an equation of tangent lines

  1. Dec 5, 2011 #1
    Having trouble with this:

    Given an ellipse (x^2/a^2) + (y^2/b^2) = , a!=b. Find the equation of the set of all points from which the two tangents to the curve are perpendicular.

    I tried finding the slope of the equation then knowing that perpendicular line are the opposite reciprocal. But still clueless on how to put it together.

    Thanks in advance
     
  2. jcsd
  3. Dec 5, 2011 #2

    HallsofIvy

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    The points in question are not on the ellipse. Suppose [itex](x_0, y_0)[/itex] is a point not on the ellipse. Then there are two lines tangent to the ellipse through [itex](x_0, y_0)[/itex]. What are there equations? What must be true if those two lines are perpendicular?
     
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