Cartesian equation: y = mx + c or x = t, y = mt +c
Click below to see one of the Associated curves.
Definitions of the Associated curves Evolute Involute 1 Involute 2 Inverse curve wrt origin Inverse wrt another circle Pedal curve wrt origin Pedal wrt another point Negative pedal curve wrt origin Negative pedal wrt another point Caustic wrt horizontal rays Caustic curve wrt another point
In fact nobody attempted a general definition of a curve until Jordan in his Cours d'Analyse in 1893.
The inverse of a straight line is a circle if the centre of inversion is not on the line.
The negative pedal of the straight line is a parabola if the pedal point is not on the line.
Since normals to a straight line never intersect and tangents coincide with the curve, evolutes, involutes and pedal curves are not too interesting.
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