Witch of Agnesi (1748) (called also "versiera")

1) fixed circle centered at A(0,a), tangent to the x-axis at the origin O

2) point Q on the circle

3) line s through the origin O and this point Q

4) tangent r to the circle, parallel to the x-axis

5) point B, intersection of lines r and s

6) line t orthogonal to r, passing through B

8) point P: projection of Q at t

The locus of points P corresponding to points Q on the circle is the curve named [ witch of Agnesi ]. In parametric form it is given by ( 2*a*t, 2*a/(1+t^2)). It can be expressed also as graph of the function f(x) = (8*a^3)/(x^2+4*a^2).

To see the animation, select the move tool (Ctrl-2) and drag point Q. To change the shape of the curve drag point A(0,a).

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