Parameterise the circle that results from intersecting the unit sphere in $\displaystyle \mathbb{R}^3$ centered at the origin with the plane $\displaystyle [(x,y,z) \in : x = z ]$

I tried $\displaystyle x^2 + y^2 + z^2 = 1 \Rightarrow 2x^2 + y^2 = 1$

however the last equation is an ellipse????