Witch of Agnesi
- Cartesian equation:
- or parametrically:
DescriptionThis was studied and named versiera by Maria Agnesi in 1748 in her book Istituzioni Analitiche. It is also known as Cubique d'Agnesi or Agnésienne. There is a discussion on how it came to be called witch in Agnesi's biography.
The curve had been studied earlier by Fermat and Guido Grandi in 1703.
The curve lies between and . It has points of inflection at . The line is an asymptote to the curve.
The curve can be considered as the locus of a point defined as follows. Draw a circle with centre at through . Draw a line from cutting at and the line at . Then has the -coordinate of and the -coordinate of .
The tangent to the Witch of Agnesi at the point with parameter is
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