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anonymous

  • one year ago

What is the standard equation of a circle?

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  1. Michele_Laino
    • one year ago
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    here is the standard equation of a circle: \[\Large {x^2} + {y^2} + ax + by + c = 0\] where, a, b, and c are real coefficient, which satisfy that condition: \[\Large \frac{{{a^2}}}{4} + \frac{{{b^2}}}{4} - c > 0\]

  2. Michele_Laino
    • one year ago
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    coefficients*

  3. anonymous
    • one year ago
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    I always thought the "standard form" of the equation of a circle was\[\left( x-a \right)^{2} + \left( y-b \right)^{2} = r ^{2}\]where the center of the circle is at (a, b) and the radius is r.

  4. anonymous
    • one year ago
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    Haha, me too...

  5. freckles
    • one year ago
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    I think the first way mentioned by Michele is the general form and the way mentioned by osprey is the standard form. Though I'm not sure if these terms hold universal.

  6. anonymous
    • one year ago
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    @Michele_Laino 's equation results in an ellipse.

  7. anonymous
    • one year ago
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    Ok, think I got the answer, thanks!

  8. Michele_Laino
    • one year ago
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    please, note that, my equation is not the equation of an ellipse @ospreytriple

  9. anonymous
    • one year ago
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    Let a=4, b=3, and c=1, for example. Graph it and see what you get, @Michele_Laino

  10. Michele_Laino
    • one year ago
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    that is a condition, on parameters a, b, and c

  11. anonymous
    • one year ago
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    ???? If the equation truly represents a circle, then the values of a, b, and c shouldn't matter so long as they satisfy the condition you mentioned. It should always produce a circle. And it doesn't.

  12. freckles
    • one year ago
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    Michele_Laino has written general form for equation @ospreytriple \[x^2+y^2+ax+by+c=0 \\ x^2+ax+y^2+by=-c \\ (x^2+ax+(\frac{a}{2})^2)+(y^2+by+(\frac{b}{2})^2)=-c +(\frac{a}{2})^2+(\frac{b}{2})^2 \\ (x+\frac{a}{2})^2+(y+\frac{b}{2})^2 =\frac{a^2}{4}+\frac{b^2}{4}-c \\ \text{ center is } (\frac{-a}{2},\frac{-b}{2}) \\ \text{ and radius is } \sqrt{\frac{a^2}{4}+\frac{b^2}{4}-c} \\ \text{ this is a circle if } \frac{a^2}{4}+\frac{b^2}{4}-c>0 \]

  13. freckles
    • one year ago
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    general form for circle *

  14. freckles
    • one year ago
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    http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%2B4x%2B3y%2B1%3D0 the example you picked shows a circle

  15. anonymous
    • one year ago
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    Must be something wrong with my version of Autograph as it clearly shows an ellipse. If so, please accept my apologies. I do, however, stand by my "standard form" equation.

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