Question:

To determine symmetry of a locus, we check if replacing coordinates with their symmetric counterparts yields the same equation. For symmetry about the x-axis, we replace $y$ with $-y$; if the equation remains unchanged, the locus is symmetric about the x-axis. For symmetry about the y-axis, we replace $x$ with $-x$. For symmetry about $y=x$, we swap $x$ and $y$. For symmetry about the origin, we replace both $x$ with $-x$ and $y$ with $-y$. Without the explicit locus equation in this problem, the correct answer being the x-axis suggests that the original equation contains only even powers of $y$ or is independent of $y$'s sign, making it symmetric about the x-axis.