Conchoid of de Sluze

The conchoid of de Sluze is a family of plane curves was investigated in 1662 by René François Walther de Sluze. In polar coordinates, it is expressed as follows:

For Cartesian coordinates the following applies:

However, the Cartesian form has a solution point, which is not present in the polar coordinate form.

These expressions have an asymptote ( for ). The point that is farthest from the asymptote a,. Add to curves intersect itself

The area between the curve and the asymptote is calculated as follows:

Is the area of ​​the loop

Four curves of the family have special names:

  • , Straight line ( asymptote for the rest of the band )
  • , Cisoids ( clue to geometric construction)
  • , Right strophoid
  • , Trisektrix of Maclaurin
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