Find a vector function that represents the curve of intersection of $x^2+y^2=4$ and $z=x$

Question

Find a vector function that represents the curve of intersection of $x^2+y^2=4$ and $z=x$

I changed $x^2+y^2=4$ to $4sin^2\theta + 4cos^2\theta = 4$ so $x=2cos\theta$ and $y=2sin\theta$ and then $z=2cos\theta$

so my overall answer was $R= <2cos\theta,2sin\theta,2cos\theta>$

i got $0$ points on this problem on my exam so i'm assuming i did the problem completely wrong.