Curve of intersection with 2 surfaces

Show that the curve with vector equation

is the curve of intersection of the surfaces http://latex.codecogs.com/png.latex?...+y%5E2%20=%201 and http://latex.codecogs.com/png.latex?...0z%5E2%20=%204.

Attempt:

(1)

(2)

plug (1) into (2) for y

Expanding and canceling

(3)

vector equation

(4)

plug (4) into (3)

divide out the 4

identity

therefore 1= 1

Did i even do this correct?

If not where did i go wrong?

Thank you

1 Attachment(s)

Re: Curve of intersection with 2 surfaces

Hi,

Here are some helpful comments, I hope.

Attachment 28441