Answer
x-axis only.
Work Step by Step
Step 1. To test symmetry with respect to the x-axis, replace $(x,y)$ with $(x,-y)$, we have: $x+(-y)^2=10$ which is the same as the original, thus it is symmetric with respect to the x-axis.
Step 2. To test symmetry with respect to the y-axis, replace $(x,y)$ with $(-x,y)$, we have: $-x+(y)^2=10$ which is different from the original, thus it is not symmetric with respect to the y-axis.
Step 3. To test symmetry with respect to the origin, replace $(x,y)$ with $(-x,-y)$, we have: $-x+(-y)^2=10$ which is different from the original, thus it is not symmetric with respect to the origin.
Step 4. Thus the equation has a symmetry with respect to the x-axis only.