# Changing the variables

We define a new coordinate system in which and are tilted at 45 degrees relative to and This gives us

Substituting this into our expression for the envelope curve

gives

This is the equation of a parabola.

Home ›

We define a new coordinate system in which and are tilted at 45 degrees relative to and This gives us

Substituting this into our expression for the envelope curve

gives

This is the equation of a parabola.