CALCULATOR
General Circle Radius with Negative Constant Calculator
General Circle Radius with Negative Constant. Example: Linear x: 6 m, Linear y: 8 m, Constant magnitude: 75 m² gives 10 m. Constant F=-q<0 explicitly parameterized; general positive-F existence checks deferred. Original useful product scope; historical catalog title does not grant missing modes or source parity.
Constant F=-q<0 explicitly parameterized; general positive-F existence checks deferred. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Completing both squares gives center (-D/2,-E/2) and positive radius.
Accepted inputs: Linear x: -100 to 100 m; Linear y: -100 to 100 m; Constant magnitude: 0.1 to 10,000 m².
How the calculation works
x²+y²+D x+E y-q=0 ⇒ r=√(D²/4+E²/4+q)
Worked example
With linear x 6 m, linear y 8 m, constant magnitude 75 m², general circle radius with negative constant is 10 m.
Assumptions and limits
Constant F=-q<0 explicitly parameterized; general positive-F existence checks deferred. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Completing both squares gives center (-D/2,-E/2) and positive radius.