Answer
Elliptical paraboloid
Work Step by Step
Subtract 4 and divide with (-4)
$\displaystyle \frac{x-4}{-4}=\frac{y^{2}}{1^{2}}+\frac{z^{2}}{2^{2}}$
We compare with Table 12.1 and, after interchanging x and z,
conclude that this is an elliptical paraboloid, which opens toward the negative direction of x.
The vertex is shifted 4 units in the +x direction.
The traces in xy and xz planes are parabolas.
The traces in planes parallel to the yz plane are ellipses.
