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See also:WITCH OF See also:AGNESI , in See also:geometry, a cubic See also:curve invented by Maria Gaetana See also:Agnesi . It is constructed by the following method: Let See also:AQB be a semicircle of See also:diameter AB, produce MQ the See also:ordinate of Q to P so that MQ : MP :: AM : AB . Then the See also:locus of P is the See also:witch . The cartesian See also:equation, if A be taken as origin and AB(=2a) for the See also:axis of x, is xy2=4a2(2a-x) . The curve consists of one See also:branch entirely to the See also:left of the See also:line x=2a and having the axis of y as an asymptote . |
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