Cartesian equation: y(x
+a) = a
or x = at, y = a/(1+t)
Click below to see one of the Associated curves.
Definitions of the Associated curves Evolute Involute 1 Involute 2 Inverse curve wrt origin Inverse wrt another circle Pedal curve wrt origin Pedal wrt another point Negative pedal curve wrt origin Negative pedal wrt another point Caustic wrt horizontal rays Caustic curve wrt another point
The curve had been studied earlier by Fermat and Guido Grandi in 1703.
The curve lies between y = 0 and y = a. It has points of inflection at y = 3a/4. The line y = 0 is an asymptote to the curve.
The curve can be considered as the locus of a point P defined as follows. Draw a circle C with centre at (0,a/2) through O. Draw a line from O cutting C at L and the line y = a at M. Then P has the x-coordinate of M and the y-coordinate of L.
The tangent to the Witch of Agnesi at the point with parameter p is
(p+1)y + 2px = a(3p+1).
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