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

A)An elliptic cylinder
B)A sphere
C)A parabolic cylinder
D)An elliptic cone
E)An ellipsoid

Question

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

A)An elliptic cylinder
B)A sphere
C)A parabolic cylinder
D)An elliptic cone
E)An ellipsoid

Quizplus · Accepted Answer

The given equation $z^2 = \frac{x^2}{4} + \frac{y^2}{16}$ represents an elliptic cone. This is because it is of the form $z^2 = Ax^2 + By^2$, which is the standard form of a cone in three-dimensional space.

In the Three-Dimensional Euclidean Space, the Graph Of z2=x24+y216z ^ { 2 } = \frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 }z2=4x2​+16y2​

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