Finding the Normal Plane to a Curve Given in Parametric Coordinates

The normal plane to a curve at a point is defined as the plane containing the principal normal to the curve at the point and perpendicular to the tangent vector at the point.

To find the equation of the normal plane to the curveat the point(where), take a pointin the plane thenis a vector in the tangent plane.

A tangent vector to the curve is given by

The normal plane is then given by

This simplifies to