How Many Conditions Are Needed to Specify a Circle?

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SUMMARY

The discussion clarifies that while the general equation of a circle involves three constants, only three conditions are necessary to specify a circle: the center's coordinates (two pieces of information) and the radius. Specifically, three points on the circle can also be used to derive the center and radius through a system of equations. Thus, the conclusion is that three conditions are required to fully define a circle in a two-dimensional space.

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the general equation of a circle has 3 constants , so it is said that 3 conditions , like 3 points (on the circle) are required to specify a circle , but , we require only the center and radius to specify a circle , so how many conditions are actually required ??
 
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The center is two pieces of information, an x-coordinate and a y-coordinate, thus three total. If you have x-y coordinates of 3 points, you can write 3 equations with 3 unknowns and solve for the radius and the coordinates of the center.

See this thread:

https://www.physicsforums.com/showthread.php?t=24014
 

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