Show that if a surface is tangent to a plane along a curve, then the points of this curve are either parabolic or planar.

Defition: A point of a surface is parabolic if $\displaystyle det(dN_p) = 0$ with $\displaystyle dN_p$ =/= $\displaystyle 0$. A point of a surface is planar if $\displaystyle dN_p = 0$.