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Math Help - conics

  1. #1
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    conics

    Given that the parabolas

    x^2 = y + 2
    y^2 = x + 3

    meet in four points, show that these four points lie on a circle, and also on a
    rectangular hyperbola.
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  2. #2
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    Quote Originally Posted by millwallcrazy View Post
    Given that the parabolas

    x^2 = y + 2
    y^2 = x + 3

    meet in four points, show that these four points lie on a circle, and also on a
    rectangular hyperbola.
    Add the two equations together: x^2 + y^2 = y + x + 5. Any point that satisfies the original two equations will also satisfy that new equation. But that new equation is the equation of a circle. So any point that lies on both parabolas also lies on the circle.

    If you subtract the equations instead of adding them, you'll get the equation of a rectangular hyperbola... .
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