symmetry to eithr x,y axis or origin

[har]

I am having trouble finding the proper order pairs algebraically.
the question is to test the equation 9y^2-4x^2=36 for symmetry on respect with to the x axis, y axis, and the origin and then graph it.
Well I figured out that it was symmetric to the origin because if you change both the x with -x and y with -y the equation is still true.
I made a table with figures that worked with this equation. the problem I am having is that when I try and figure out the y or x value with algerbra I am not getting the right result.
I'll us x as 3 as an example,the y value should be 0
9y^2-4(3)^2= 36
9y^2-36=36
9y^2=72
I squared both sides
3y=8.485...
that does not come out to be 0 and I dont know where I have made the mistake

 

[galactus]

The reason it does not work is because if x=0, then y=2.

Yes, it is symmetric about the origin.

Solve it for y and graph to see what is going on.

\(\displaystyle y=\frac{\pm 2\sqrt{x^{2}+9}}{3}\)

Now, plug in any x value and you get your y.

Note, if x=3, then y=\(\displaystyle 2\sqrt{2}\)

 

[Deleted member 4993]

I am having trouble finding the proper order pairs algebraically.
the question is to test the equation 9y^2-4x^2=36 for symmetry on respect with to the x axis, y axis, and the origin and then graph it.
Well I figured out that it was symmetric to the origin because if you change both the x with -x and y with -y the equation is still true.
I made a table with figures that worked with this equation. the problem I am having is that when I try and figure out the y or x value with algerbra I am not getting the right result.
I'll us x as 3 as an example,the y value should be 0
9y^2-4(3)^2= 36
9y^2-36=36
9y^2=72
I squared both sides
3y=8.485...
that does not come out to be 0 and I dont know where I have made the mistake

Using a graph-paper or graphing calculator - plot the function (It is "theoretically" not a function - fails vertical line test).

Then you'll see clearely - that it is a hyperbola and the range of the function does not include that point (range excudes |y|<2).

 

[har]

Thank you Galactus
I see how that works now. Where did that formula come from/ what is it called?