INVERSION : Summary

If you have studiously worked through the inversion constructions for all our curves, you may by now feel quite confused! Below is a table which summarizes all the results we have found so far.

In the table we have used the notation O to denoted the centre of a curve, C to denote a cusp, F to denote a focus, N to denote a node, V to denote a vertex – all where applicable.

CURVES AND THEIR INVERSES

 

Astroid

Cardioid

Cardioid

 Centre

Hyperbola 

Cardioid

Cusp

Parabola

Circle

Any point

Circle

Ellipse

 Focus

Limaçon 

Hyperbola

Graph vertex 

Right Strophoid

Rectangular Hyperbola

Centre

Lemniscate

Lemniscate

 Centre

Rectangular Hyperbola 

Limaçon

Node 

Parabola 

Parabola

 Focus

Cardioid

Parabola

Vertex

Cissoid of Diocels