Question

Consider the equation $$x^2+y^2 =4 $$

(a) What does this equation represent in a two-

dimensional system?

b) What does this equation represent in a three-

dimensional system?

Short answer

The given equation represents a circle in a 2D system and it represents a cylinder in a 3D system.

Step-by-step solution

Step 1. Part (a) of the question.

The given equation is:

$${x}^2 + {y}^2 = 4 $$

The above equation represents a circle with its center at (0,0) in a two-dimensional system.

Step 2. Part (b) of the question 

The given equation $$x^2+y^2 =4 $$ represents a cylinder in a three-dimensional system.