Identify the following quadric surface. $\frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 10 } - \frac { z ^ { 2 } } { 6 } = 1$
A) ellipsoid
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of one sheet
E) hyperboloid of two sheets

Question

Quizplus · Accepted Answer

The given equation $\frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 10 } - \frac { z ^ { 2 } } { 6 } = 1$ represents a hyperboloid of two sheets because it has terms of $x^2$, $y^2$, and $z^2$ with two of them having opposite signs and one being positive, which is characteristic of a hyperboloid of two sheets.

Identify the Following Quadric Surface x26−y210−z26=1\frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 10 } - \frac { z ^ { 2 } } { 6 } = 16x2​−10y2​−6z2​=1

Identify the Following Quadric Surface $\frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 10 } - \frac { z ^ { 2 } } { 6 } = 1$