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Conchoids of line with common center.

  Fixed point $O$

  Given curve
Each pair of coloured curves is length $d$ from the intersection with the line that a ray through $O$ makes.
   $d >$ distance of $O$ from the line

   $d =$ distance of $O$ from the line

   $d <$ distance of $O$ from the line

Conchoid of Nicomedes drawn by an apparatus illustrated in Eutocius' Commentaries on the works of Archimedes

In geometry, a conchoid is a curve derived from a fixed point $O$ , another curve, and a length $d$ . It was invented by the ancient Greek mathematician Nicomedes.^[1]

^ Chisholm, Hugh, ed. (1911). "Conchoid" . Encyclopædia Britannica. Vol. 6 (11th ed.). Cambridge University Press. pp. 826–827.