I have been struggling with this Calc III problem.
The intesection of two surfaces consists of two curves.$$x^2 + \frac{y^2}{2} = 1$$ $$z^2 + \frac{y^2}{2} = 1$$ Parameterize each curve in the form (vector)$$r(t)=\left\langle x(t),y(t),z(t)\right\rangle $$
What I have done $$x^2+\frac{y^2}{2}=z^2+\frac{y^2}{2}$$ $$\sqrt x = \sqrt z$$ $$z=x, z=-x$$------------------------------------------------------------------------------------------------------------- $$2t^2+y^2=2$$$$y^2=2-2t^2$$ $$y=\sqrt {2-2t^2}$$
But now when I try to solve for x and z I cannot figure out how to get them in terms of t. Perhaps I am overthinking this. I am not sure. Any help would be appreciated!