Answer: The lines of symmetry are x = 0 and y = 0.
Step-by-step explanation: The given equation of the curve is
[tex]x^2-y^2=16.~~~~~~~~~~~~~~~(i)[/tex]
We are to find the lines of symmetry of the above curve.
Substituting x = -x in equation (i), we have
[tex](-x)^2-y^2=16\\\\\Rightarrow x^2-y^2=16~~~~~~~~~~~~~~~~~(ii)[/tex]
and substituting y = -y in equation (i), we have
[tex]x^2-(-y)^2=16\\\\\Rightarrow x^2-y^2=16~~~~~~~~~~~~~~~~~(iii)[/tex]
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.
Answer: D
It has two lines of symmetry, the x-axis, and the y-axis.
Step-by-step explanation: I just did it
