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Intersection of a line and circle

  1. Sep 19, 2011 #1
    1. The problem statement, all variables and given/known data

    The line x+y=2a-1 intersects the circle x2+y2=a2+3a-3 at point (m,n). When m*n reaches its minimum value, what is the value of a?

    2. Relevant equations

    Equation One

    x + y = 2a - 1

    Equation Two

    x2 + y 2 = a 2 + 3a - 3
    Last edited: Sep 19, 2011
  2. jcsd
  3. Sep 19, 2011 #2


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    Science Advisor

    Square your linear (first) equation, using the fact that (x+y)^2 = x^2 + y^2 + 2xy, at which point you can easily eliminate "x^2 + y^2" from the two equations. Now you have "xy" as a function of "a" and the rest should be easy.
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