Answer
Elliptical paraboloid
Work Step by Step
Subtract 1 and divide with (-1):
$\displaystyle \frac{y-1}{-1}=\frac{x^{2}}{1^{2}}+\frac{z^{2}}{1^{2}}$
We compare with Table 12.1 and, after interchanging y and z, conclude that this is an elliptical paraboloid, which opens toward the negative direction of y. The vertex is shifted 1 unit in the +y direction.
The traces in xy and yz planes are parabolas.
The traces in planes parallel to the xz plane are ellipses.
