in . In this case, the definition amounts to being a double root of , so the equation of the envelope can be found by setting the discriminant of to (because the definition demands at some and first derivative i.e. its value and it is min/max at that ).

For example, let be the line whose and intercepts are and , this is shown in the animation above. The equation of is
:or, clearing fractions,
:The equation of the envelope is then
:

Often when is not a rational function

1.Previous
3.Next