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

A)An elliptic cone
B)A hyperboloid of one sheet
C)A circular cylinder
D)A hyperboloid of two sheets
E)An elliptic paraboloid

Question

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

A)An elliptic cone
B)A hyperboloid of one sheet
C)A circular cylinder
D)A hyperboloid of two sheets
E)An elliptic paraboloid

Quizplus · Accepted Answer

The equation $x^2 + \frac{y^2}{4} - \frac{z^2}{9} = 1$ 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 x2+y24−z29=1x ^ { 2 } + \frac { y ^ { 2 } } { 4 } - \frac { z ^ { 2 } } { 9 } = 1x2+4y2​−9z2​=1

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