What would be general formula of a circle in form of variables ?

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SUMMARY

The general formula for a circle in the Cartesian coordinate system is expressed as x² + y² = r², where r represents the radius. For circles not centered at the origin, the more general equation is (x - h)² + (y - k)² = r², where (h, k) denotes the center coordinates. This formula allows for the representation of circles in any position within the x-y plane, expanding the utility of circle equations in geometry.

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  • Understanding of Cartesian coordinates
  • Familiarity with basic algebraic equations
  • Knowledge of geometric concepts related to circles
  • Ability to manipulate quadratic equations
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  • Research the derivation of the circle equation from the distance formula
  • Explore transformations of the circle equation for different center points
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Students studying geometry, mathematics educators, and anyone interested in the properties and equations of circles in the Cartesian plane.

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General formula of a line is ax+b=0
Similarly can we have a general formula of a circle ?
 
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The general formula for a line in a plane is y=mx+c
The general formula for a circle in the x-y plane is x^2+y^2=r^2 (where r is the radius of the circle)
 
HomogenousCow said:
The general formula for a line in a plane is y=mx+c
The general formula for a circle in the x-y plane is x^2+y^2=r^2 (where r is the radius of the circle)

There's an even more general equation for a circle, one whose center is not located at the origin. :smile:
 

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