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anonymous
 one year ago
What is the standard equation of a circle?
anonymous
 one year ago
What is the standard equation of a circle?

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1here 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: \[\Large \frac{{{a^2}}}{4} + \frac{{{b^2}}}{4}  c > 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I always thought the "standard form" of the equation of a circle was\[\left( xa \right)^{2} + \left( yb \right)^{2} = r ^{2}\]where the center of the circle is at (a, b) and the radius is r.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0I 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino 's equation results in an ellipse.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, think I got the answer, thanks!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please, note that, my equation is not the equation of an ellipse @ospreytriple

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let a=4, b=3, and c=1, for example. Graph it and see what you get, @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that is a condition, on parameters a, b, and c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0???? 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.

freckles
 one year ago
Best ResponseYou've already chosen the best response.0Michele_Laino has written general form for equation @ospreytriple \[x^2+y^2+ax+by+c=0 \\ x^2+ax+y^2+by=c \\ (x^2+ax+(\frac{a}{2})^2)+(y^2+by+(\frac{b}{2})^2)=c +(\frac{a}{2})^2+(\frac{b}{2})^2 \\ (x+\frac{a}{2})^2+(y+\frac{b}{2})^2 =\frac{a^2}{4}+\frac{b^2}{4}c \\ \text{ center is } (\frac{a}{2},\frac{b}{2}) \\ \text{ and radius is } \sqrt{\frac{a^2}{4}+\frac{b^2}{4}c} \\ \text{ this is a circle if } \frac{a^2}{4}+\frac{b^2}{4}c>0 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0general form for circle *

freckles
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2%2B4x%2B3y%2B1%3D0 the example you picked shows a circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Must 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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