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

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

Question

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

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

Quizplus · Accepted Answer

The equation $z = \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 }$ represents a hyperbolic paraboloid because it has opposite signs for the $x^2$ and $y^2$ terms, indicating hyperbolic cross-sections, and it is linear in $z$, indicating it is a paraboloid.

In the Three-Dimensional Euclidean Space, the Graph Of z=x24−y29z = \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 }z=4x2​−9y2​

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