Question

describe the surface and give traces :

x = y^2 - 4z^2

Answer 1

It's a hyperbolic paraboloid
for y=k, x = k^2-4z^2
for z=k, x = y^2-4k^2
both are parabolas
for x=k, y^2-4z^2 = k^2
is a hyperbola