Step-by-step explanation:
First, let's find the intercepts.
The x-intercepts are the values of x when y = 0, so we need to solve the following equation:
x² + y - 121 = 0
x² + 0 - 121 = 0
x² - 121 = 0
x² - 121 + 121 = 0 + 121
x² = 121
x = ±√121
x = ±11
It means that the x-intercepts are the points (11, 0) and (-11, 0)
In the same way, we can calculate the y-intercept replacing x = 0, so:
x² + y - 121 = 0
0² + y - 121 = 0
y - 121 = 0
y - 121 + 121 = 0 + 121
y = 121
Therefore, the point (0, 121) is the y-intercept.
Now, we can test for symmetry.
To know if the equation is symmetric with respect to the x-axis, we will replace y by -y. So,
x² + (-y) - 121 = 0
x² - y - 121 = 0
Since x² - y - 121 = 0 and x² + y - 121 = 0 are distinct, the equation is not symmetric with respect to the x-axis.
In the same