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Point Circle


Members of a coaxal system satisfy

 x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0

for values of lambda. Picking lambda^2=c then gives the two circles

 (x+/-sqrt(c))^2+y^2=0

of zero radius, known as point circles. The two point circles (+/-sqrt(c),0), real or imaginary, are called the limiting points of the coaxal system.


See also

Coaxal System, Limiting Point

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References

Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, p. 123, 1928.

Referenced on Wolfram|Alpha

Point Circle

Cite this as:

Weisstein, Eric W. "Point Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PointCircle.html

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