Which of the following is the equation of the tangent plane at the point on the surface where and ?
Now, let’s find the curve on the surface associated to this curve in the domain. Set . A parameterization of the curve in the - plane is
and a parameterization of the associated curve on the surface is
To determine whether the tangent line lies on the tangent plane, we must check whether
for all .
Does the tangent line lie on the tangent plane? YesNo