\(hyperbola H = x^2-y^2=1 \)

When stretched in the x direction by \(1/3\)

it becomes \(9x^2-y=1 \)

please explain i am really confused by this as I thought in this situation you should substitute x to 3x

I would not call it streched as it is being shrunk but anyway.

\((3x)^2-y^2=1\\ is\\ 9x^2-y^2=1\)

So x is replaced by 3x just as you wanted to do :)

Thank you!