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

Algebra ->  Coordinate-system -> 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      Log On


   

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(5398) About Me  (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
%28-x%29%5E2+y%5E2%2B%28-x%29y=x%5E2y%5E2-xy and that is not the same as x%5E2y%5E2%2Bxy=8
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
%28-x%29%5E2+y%5E2%2Bx%28-y%29=x%5E2y%5E2-xy and that is not the same as x%5E2y%5E2%2Bxy=8
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
%28-x%29%5E2+y%5E2%2B%28-x%29%28-y%29=x%5E2y%5E2%2Bxy=8.
So the graph is symmetrical with respect to the origin.
graph%28300%2C300%2C-3%2C3%2C-3%2C3%2C2.37%2Fx%2C-3.37%2Fx%29