I just need to check if my work has been done accordingly.

Q: Find the vector function that represents the curve of the intersection of the 2 surfaces.

The cylinder $\displaystyle x^2 + y^2 = 4$ and $\displaystyle z= xy$

Solution:

$\displaystyle x^2 + y^2 = 4 \rightarrow x+y = 2 $

$\displaystyle x = cos(t) y=sin(t) 0 \lesseq t \lesseq \frac{pi}{2}$