Given two curves 
and 
and a fixed point 
, let a line from 
cut 
at 
and 
at 
.
Then the locus of a point 
such that 
is the cissoid. The word cissoid means "ivy shaped."
| curve 1 | curve 2 | pole | cissoid |
| line | parallel line | any point | line |
| line | circle | center of circle | conchoid of Nicomedes |
| circle | circle tangent line | on circumference | oblique cissoid |
| circle | circle tangent line | on circumference opposite tangent | cissoid of Diocles |
| circle | radial line | on circumference | strophoid |
| circle | concentric circle | center of circles | circle |
| circle | same circle |  | lemniscate |
