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

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

Question

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

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

Quizplus · Accepted Answer

The equation $4x^2 + y^2 = 16$ represents an elliptic cylinder because it is an equation of an ellipse that extends infinitely in the third dimension (along the z-axis), which is not explicitly mentioned in the equation.

In the Three-Dimensional Euclidean Space, the Graph Of 4x2+y2=164 x ^ { 2 } + y ^ { 2 } = 164x2+y2=16

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