I have an ellipsoid $$x^{2}+2y^{2}+4z^{2}=18$$ which lies right to the plane y=1 and has outward pointing orientation.
I am asked to use stoke's theorem to find $$\oint_{C} F\cdot dr = \iint_{R}\nabla \times FdS$$
but to do so a parameterisation is required such that I can express x, y and z in terms of 2 variables (I.e., u and v).
I begin first by finding the boundary C of S. To do so, I sub y =1 into the equation of the given ellipsoid. we get
$$x^{2}+4z^{2}=16$$
Edit: Aware of the standard parametrisation used in spherical and cylindrical coordiantes but unsure how I should apply these to this problem. Give me a kick