Graph x^2-y^2=16. what are its lines of symmetry

The lines of symmetry are x = 0 and y = 0.

Step-by-step explanation:  The given equation of the curve is

We are to find the lines of symmetry of the above curve.

Substituting x = -x in equation (i), we have

and substituting y = -y in equation (i), we have

We know that x = -x gives the reflection across Y-axis and y = -y gives the reflection across X-axis.

Since equations (ii) and (iii) are same as equation (i), therefore, X-axis (y = 0) and Y-axis (x = 0) are the lines of symmetry for the curve (i).

The graph of the given curve is attached below.

We can see that x = 0 and y = 0 are the only lines of symmetries of the curve.