## Thomas' Calculus 13th Edition

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.