Answer
Elliptical paraboloid
See image:
.
Work Step by Step
Subtract 1 and divide with (-1)
$\displaystyle \frac{y-1}{-1}=\frac{x^{2}}{1^{2}}+\frac{z^{2}}{2^{2}}$
Compare with Table 11.1 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 units in the +y direction.
The traces in xy and yz planes are parabolas.
The traces in planes parallel to the xz plane are ellipses.
