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Tangent Lines of Two Circles Intersect At Point

  1. Oct 20, 2012 #1
    1. The problem statement, all variables and given/known data

    The tangent lines of two circles intersect at point (11/3,2/3). What are the two points that each tangent line touches on its respective circle?

    2. Relevant equations

    Circle 1: x^2 + (y-3)^2 =5
    Circle 2: (x-2)^2 + (y+3)^2 = 2

    3. The attempt at a solution

    I found the derivatives of each circle.

    Circle 1: y'(x) = -(x)/(y-3)
    Circle 2: y'(x) = (2-x)/(y+5)

    Do I have to use the slope-intercept equation somehow? y-yo=m(x-xo)

    I'm not quite sure what do to next... :S
     
  2. jcsd
  3. Oct 21, 2012 #2
    help anyone??
     
  4. Oct 22, 2012 #3

    SammyS

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    Hello VectorCereal. Welcome to PF !

    Yes, using the slope intercept equation of a line can be helpful. In this case, (x0, y0) = (11/3, 2/3) .

    Also, it looks to me like the problem can be solved for either circle independently of the other circle.

    For Circle 1:

    If you plug y'(x) = -(x)/(y-3) in for m in the slope intercept equation, you get the equation of another circle. See where this circle intersects with Circle 1.

    Check your answer, because this seems like a weird method of solution !
     
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