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Witch of Agnesi

1911 Encyclopedia Britannica

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In geometry, a cubic curve invented by Maria Gaetana Agnesi. It is constructed by the following method: Let AQB be a semicircle of diameter AB, produce MQ the ordinate of Q to P so that MQ: MP :: AM: AB. Then the locus of P is the witch. The cartesian equation, if A be taken as origin and AB (= 2a ) for the axis of x, is xy 2 =4a2(2a - x). The curve consists of one branch entirely to the left of the line x= 2a and having the axis of y as an asymptote.