## Witch of Agnesi |

In
**Witch of Agnesi** (Italian pronunciation:

Starting with a fixed circle, a point O on the circle is chosen. For any other point A on the circle, the secant line OA is drawn. The point M is diametrically opposite to O. The line OA intersects the tangent of M at the point N. The line parallel to OM through N, and the line perpendicular to OM through A intersect at P. As the point A is varied, the path of P is the Witch of Agnesi.

The curve is

The Witch of Agnesi gets its name from Italian mathematician
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Suppose the point O is the origin, and that M is on the positive y-axis. Suppose the radius of the circle is a.

Then the curve has Cartesian equation

Note that if *a* = 1/2, then this equation becomes rather simple:

This is the derivative of the

Parametrically, if θ is the angle between OM and OA, measured clockwise, then the curve is defined by the equations

Another parameterization, with θ being the angle between OA and the x-axis, increasing anti-clockwise is

Other Languages

Afrikaans: Heks van Agnesi

български: Версиера

bosanski: Versiera

català: Corba d'Agnesi

dansk: Agnesis heks

Deutsch: Versiera der Agnesi

Ελληνικά: Μάγισσα της Ανιέσι

español: Curva de Agnesi

français: Sorcière d'Agnesi

한국어: 아녜시의 마녀

italiano: Versiera

עברית: המכשפה של אנייזי

қазақша: Аньези локоны

magyar: Agnesi-féle görbe

日本語: アーネシの曲線

norsk nynorsk: Agnesis heks

Piemontèis: Masca d'Agnesi

polski: Lok Agnesi

português: Curva de Agnesi

русский: Верзьера Аньези

slovenščina: Agnesin koder

svenska: Agnesis häxa

українська: Локон Аньєзі

中文: 箕舌线