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Homework Help: Show that 4c=1+4r^2

  1. Dec 11, 2012 #1
    1. The problem statement, all variables and given/known data

    This was a question from the HSC Advanced maths exam in Australia, the second easiest maths course.
    2. Relevant equations


    3. The attempt at a solution
    I have no idea ):
  2. jcsd
  3. Dec 11, 2012 #2


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    An idea to start is to solve the system for x and y, even though they will be in symbolic form. Notice, that in i, what you are asked to show is not expressed with x or y.
  4. Dec 11, 2012 #3


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    Find the equation that gives the solution set for the intersection points between the circle and the parabola. This is a quartic in x, reducible to a quadratic in x2. Now use the stipulation given ("located symmetrically") to deduce a condition that the discriminant of that quadratic must satisfy.

    For the second part, figure out what condition the sum of the roots of that quadratic has to satisfy.
    Last edited: Dec 11, 2012
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