[alogo] Witch of Agnesi

[0_0] [0_1] [0_2] [0_3]


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).

Produced with EucliDraw©