In the three-dimensional Euclidean space, the graph of $3 x ^ { 2 } + 3 y ^ { 2 } = 16$ is

A)A circle
B)A sphere
C)A plane
D)A circular cylinder
E)An ellipsoid

Question

In the three-dimensional Euclidean space, the graph of $3 x ^ { 2 } + 3 y ^ { 2 } = 16$ is

A)A circle
B)A sphere
C)A plane
D)A circular cylinder
E)An ellipsoid

Quizplus · Accepted Answer

The equation $3x^2 + 3y^2 = 16$ represents a circular cylinder in three-dimensional Euclidean space. This is because the equation involves two squared variables (x and y) with the same coefficient, but does not involve the z variable, meaning its shape extends infinitely along the z-axis, forming a cylinder. The absence of z indicates that the shape is the same at all values of z, characteristic of a cylinder.

In the Three-Dimensional Euclidean Space, the Graph Of 3x2+3y2=163 x ^ { 2 } + 3 y ^ { 2 } = 163x2+3y2=16

In the Three-Dimensional Euclidean Space, the Graph Of $3 x ^ { 2 } + 3 y ^ { 2 } = 16$