"Let S denote the elliptical cylinder given by the equation 4y2+ z2=4, and let C be the curve obtained by intersecting S with the plane y=x.
I am not sure how to go about this. I tried solving the equations for each other
y2= 1- z2/4
and then do i do some sort of parameterization of sqrt(1-z2/4) -x=0 or am i supposed to parameterize the cylinder and plane separately? I know the cylinder parameterizes to
but i don't know what to do from here. If anyone could hit me with some tips i would greatly appreciate it
would it simply be <cos (t), cos (t), 2 sin (t)> as x=y and y is equal to cos(t)? is it really this simple?