Question

determine whether the graph of the equation is symmetric with respect to the y - axis, the x - axis, the origin, more than one of these, or none of these.
\\(y^2 = x^2 + 17\\)
select all that apply.
\\(\square\\) x - axis
\\(\square\\) y - axis
\\(\square\\) origin
\\(\square\\) none of these

Explanation:

Step1: Test x-axis symmetry

Replace $y$ with $-y$:
$$(-y)^2 = x^2 + 17$$
Simplify to get $y^2 = x^2 + 17$, which matches the original equation.

Step2: Test y-axis symmetry

Replace $x$ with $-x$:
$$y^2 = (-x)^2 + 17$$
Simplify to get $y^2 = x^2 + 17$, which matches the original equation.

Step3: Test origin symmetry

Replace $x$ with $-x$ and $y$ with $-y$:
$$(-y)^2 = (-x)^2 + 17$$
Simplify to get $y^2 = x^2 + 17$, which matches the original equation.

Answer:

x-axis, y-axis, origin