How do I mathematically prove that y=1/x is a hyperbola?
The transformation clearly suggests that the angle of rotation is 45 degrees.
So you need to rotate the axes by 45 degrees and you can do that by changing the variables.
To visualize the equation xy=1 in the xy-plane, we can execute the transformation -- now the transformed equation becomes x'^2 - y'^2 =1 shown below in the x'y' -plane.
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The transformation clearly suggests that the angle of rotation is 45 degrees.
So you need to rotate the axes by 45 degrees and you can do that by changing the variables.
To visualize the equation xy=1 in the xy-plane, we can execute the transformation -- now the transformed equation becomes x'^2 - y'^2 =1 shown below in the x'y' -plane.
