Answer
An ellipse in the plane $y=z$.
Work Step by Step
$x^{2}+y^{2}=4$ is a cylinder with the z-axis as its axis.
$z=y$ is a plane inclined towards the xy-plane at an angle of $45^{\circ}$.
The intersection is an ellipse in the plane $y=z$ (a cross section of an upright cylinder).
See the image below.
