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Homework Help: Hyperbola in Cartesian Planes problem

  1. Jan 11, 2007 #1
    Does the plane that intersects the cone need to be parallell to the axis of the cone to make the section a hyperbola, or is it enough that it is not parallell to a generator?

    If the latter is correct, can one say that a parabola is a special case of a hyperbola?
    Last edited: Jan 11, 2007
  2. jcsd
  3. Jan 11, 2007 #2

    Gib Z

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    The Latter is correct.

    The hyperbola in Cartesian Planes is defined by Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. As you Can see, a parabola is simply where B and C equals zero.
  4. Jan 12, 2007 #3
    Thank you!
  5. Jan 12, 2007 #4

    Gib Z

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    No problemo :)
  6. Jan 12, 2007 #5


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    If one takes one of the focal points of a hyperbola to infinity, then the remaining curve would be a parabola. Same is valid for an ellipse.

    In other words let b tend to infinity in

    [tex] \frac{x^{2}}{a^{2}}\pm \frac{y^{2}}{b^{2}} =1 [/tex]

    and you'll get a parabola.

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