cylinder has guidelines for curve x^2+y^2=4,x-y=0, perpendic

[Apprentice123]

A cylinder has guidelines for the curve \(\displaystyle \begin{cases}x^2+y^2=4 \\ x-y=0\end{cases}\) and its generating are perpendicular to the plane of the guideline. Determine your equation

Answer:
\(\displaystyle x^2+y^2+2xy-8z=0\)