In the three-dimensional Euclidean space, the graph of $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } - \frac { z ^ { 2 } } { 16 } = 1$ is

A)An elliptic cylinder
B)A hyperboloid of one sheet
C)A hyperbolic cylinder
D)A hyperboloid of two sheets
E)An ellipsoid

Question

In the three-dimensional Euclidean space, the graph of $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } - \frac { z ^ { 2 } } { 16 } = 1$ is

A)An elliptic cylinder
B)A hyperboloid of one sheet
C)A hyperbolic cylinder
D)A hyperboloid of two sheets
E)An ellipsoid

Quizplus · Accepted Answer

The given equation $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } - \frac { z ^ { 2 } } { 16 } = 1$ represents a hyperboloid of one sheet. This is because it has two squared terms with positive coefficients and one squared term with a negative coefficient, which is characteristic of a hyperboloid of one sheet.

In the Three-Dimensional Euclidean Space, the Graph Of x24+y29−z216=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } - \frac { z ^ { 2 } } { 16 } = 14x2​+9y2​−16z2​=1

In the Three-Dimensional Euclidean Space, the Graph Of $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } - \frac { z ^ { 2 } } { 16 } = 1$