Which of the following is the equation of the tangent plane at the point on the surface where and ?

none of these
Does the point lies on the curve ? YesNo

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

Find a parametric description of the tangent line to the curve in the previous part at the point .

What must be so ? You can use any of the components of (although one allows for an efficient computation) to find that .
A vector parallel to the tangent line is .

Use where .

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