What is a symmetric equation?

A symmetric equation is a mathematical expression that remains unchanged when the variables are interchanged. In the context of geometry, particularly in three-dimensional space, it often describes a surface or curve where the relationship between the variables is invariant under symmetry operations, such as reflection or rotation. For example, the equation (x^2 + y^2 = r^2) is symmetric with respect to the x-axis and y-axis, representing a circle centered at the origin.