Conic Command

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Conic[ <Point>, <Point>, <Point>, <Point>, <Point> ]
Returns a conic section through the five given points.
Example: Conic[(0, -4), (2, 4), (3,1), (-2,3), (-3,-1)] yields 151x² - 37x y + 72y² + 14x - 42y = 1320 .
Note: If four of the points lie on one line, then the conic section is not defined.
Conic[ <Number a>, <Number b>, <Number c>, <Number d>, <Number e>, <Number f> ]
Returns a conic section \mathrm{\mathsf{ a\cdot x^2+d\cdot xy+b\cdot y^2+e\cdot x+f\cdot y=-c }}.
Example: Conic[2, 3, -1, 4, 2, -3] yields 2x² + 4x y + 3y² + 2x - 3y = 1 .
Note: See also Mode conic5.svg Conic through 5 Points tool and Coefficients command.
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