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Math Help - Conic Sections

  1. #1
    Senior Member Stroodle's Avatar
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    Conic Sections

    Hi.

    I'm just starting to learn about conic sections, and it says in my text that their general equation is a^2+by^2+2gx+2fy+c=0.

    Is that an error? Isn't it supposed to be ax^2 not just a^2 ?

    Thanks for your help.
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  2. #2
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    Yes, the x-squared is missing. Also, the xy term is missing. In my book the general form of a quadratic equation in 2 variables is
    Ax^2 +Bxy +Cy^2 + Dx + Ey + F = 0.

    After a Google Search, I have found this equation also expressed as
    ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0,
    which is closer to what you have.


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  3. #3
    Senior Member Stroodle's Avatar
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    Awesome. Thanks for that.

    Would the xy term be present for hyperbolas and ellipses also? As my text says that this general equation is for all conic sections...
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  4. #4
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    Quote Originally Posted by Stroodle View Post
    Awesome. Thanks for that.

    Would the xy term be present for hyperbolas and ellipses also? As my text says that this general equation is for all conic sections...
    Yes.

    Actually, now that I think about it, if there is an xy term then the conic is rotated by some angle. You stated that you're starting to learn about conic sections, so the book probably omitted the xy term deliberately. This means that in parabolas & hyperbolas, without the xy term, the curves will only open upward/downward/left/right. And in ellipses, the major/minor axes will only be horizontal/vertical lines.


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  5. #5
    Senior Member Stroodle's Avatar
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    Cool. Thanks for your help!
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