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The equation is $\"\"$ .

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Observe the graph:

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The equation $\"\"$ is symmetric with respect to the origin.

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Numerical support :

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Symmetry about $\"\"$ -axis is $\"\"$ .

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Observe the point $\"\"$ is on the graph and $\"\"$ is not on the graph.

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The graph is not symmetric with respect to the $\"\"$ -axis.

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Symmetry about $\"\"$ -axis is $\"\"$ .

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Observe the point $\"\"$ is on the graph and $\"\"$ is not on the graph.

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The graph is not symmetric with respect to the $\"\"$ -axis.

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Symmetry about origin is $\"\"$ .

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Observe the point $\"\"$ is on the graph and $\"\"$ is also on the graph.

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The graph is symmetric with respect to the origin.

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Test algebraically :

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Test algebraically symmetric with respect to the $\"\"$ -axis.

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Substitute $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Because $\"\"$ is not equivalent to $\"\"$ , the equation is not symmetric with respect to $\"\"$ -axis.

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Test algebraically symmetric with respect to the $\"\"$ -axis.

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Substitute $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Because $\"\"$ is not equivalent to $\"\"$ , the equation is not symmetric with respect to $\"\"$ -axis.

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Test algebraically symmetric with respect to the origin.

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Substitute $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Because $\"\"$ is equivalent to $\"\"$ , the equation is symmetric with respect to the origin.

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The equation $\"\"$ is symmetric with respect to the origin.