Witch of Agnesi

Parametric Equations,Calculus and Analytic GeometryThe so-called "witch of Agnesi" is the red curve in the image. If the blue circle has radius r , let P be a point on the upper purple line y=2r . The red point has the same x coordinate as P. Its y coordinate has the y value of the intersection of the circle with the line connecting P with the base of the circle. The curve was studied in the mid-eighteenth century by the Italian mathematician Maria Agnesi. The label "witch" comes from a mistranslation of her workComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic