Question

Identify and trace the conicoid y2 + z2 = x. Describe its sections by the planes x = 0,y = 0 and z = 0.

Answer 1

$x=y^2+z^2$ is a paraboloid with vertex at (0, 0, 0) opening away from the origin centered on the line $y=z=0$.

When $x=0$, $0=y^2+z^2$ which means $y=z=0$, so that this section is a single point, (0, 0, 0).

When $y=0$, $x=z^2$ which is a parabola in the $x$-$z$ plane with vertex at (0, 0, 0).

When $z=0$, $x=y^2$ and this section is the same as the previous one, but lying in the the $x$-$y$.