Algebraic equation in two variables such that the graphical representation of the corresponding function in the Cartesian plane remains the same when the two variables are interchanged.

### Examples

- The equation
*x*² +*y*² = 100 is a symmetric equation. It is the equation of the relationship whose Cartesian graph is a circle centred at the origin and whose radius measures 10 units

- Consider the equation
*y*= 0.5*x*² – 3.

The graphical representation of the corresponding function*f*(*x*) = 0.5*x*² – 3 is shown in red in the graph below :

Interchanging the two variables produces the equation*x*= 0.5*y*² – 3.

The corresponding function is \(f\left( x\right) =\pm \sqrt {2x+3}\) whose graphical representation, in blue, is shown in the diagram above.

Therefore, the equation*y*= 0.5*x*² – 3**is not symmetric**since the graphs are not identical.