SOLUTION: For the graph of the equation , (x^2)(y^2)+ (xy)= 8 Is the graph symmetric with respect to the X-axis? Yes or No? Is the graph symmetric with respect to the Y-axis? Yes or No? I

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Question 624350: For the graph of the equation , (x^2)(y^2)+ (xy)= 8
Is the graph symmetric with respect to the X-axis? Yes or No?
Is the graph symmetric with respect to the Y-axis? Yes or No?
Is the graph symmetric with respect to the Origin? Yes or No?

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!

Substituting -x for x, keeping the same y means switching the point to its image on the other side of the y-axis
(like going from point A to point B or viceversa).
If we do that, we get
and that is not the same as
The graph is not symmetrical with respect to the x-axis.

Substituting -y for y, keeping the same x means switching the point to its image on the other side of the x-axis
(like going from point A to point C or viceversa).
If we do that, we get
and that is not the same as
The graph is not symmetrical with respect to the y-axis.

Substituting -x for x, and -y for y at the same time means moving to the point across the origin to the other side
(like going from point A to point D or viceversa).
If we do that, we get
.
So the graph is symmetrical with respect to the origin.