Ellipsohyperbola

Hi Valery.

Well. This curve is an example about the huge power of geometry: what you can do very easy in the paper or eventually in your garden, it requires a complete computational set for doing it analytically.

In the attached word document, the cartesian and polar expressions for the plane curve f(x,y) with foci's at origin, (b,0), with constant length equals to a.

Both have degree 8 in x,y and rho. f(x,y) have 363 therm's while f(rho,phi) have 303.

The hole for some values of the constant distance between points ensure that it is not an analytical plane curve path.

Best regards.

Alvaro.

Hi.

Attached gives a more efficient point - finder routine. The routine also purge for complexes. As a matrix of x,y values, it can be also augmented by any other routine that found valid points.

Best regards.

Alvaro.