Answer
The intersection is an ellipse in the plane $y=z,$
(a cross section of an upright cylinder)
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 $45^{\circ.}$.
See image below.
The intersection is an ellipse in the plane $y=z,$
(a cross section of an upright cylinder).
