Witch of Agnesi

The so-called "witch of Agnesi" is the red curve in the image. If the blue circle has radius , let P be a point on the upper purple line . The red point has the same coordinate as P. Its coordinate has the 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 work.