How do we draw the "left and right" contours of a hyperbolic function?
I have been stumped on problem 3 for today's problem set, where we are to sketch a contour diagram of $f(x,y) = 4x^2 - 9y^2$. I know how to find the asymptotes (by setting $f(x,y) = 0$ and solving for $y$, which gives you asymptotes of $$y =\pm \frac{2}{3} x$$ which are very easy to plot). I can then solve for the "top and bottom" hyperbola by setting $f(x,y) = 1$, and solving for $y$ which gives "top and bottom" contours of $$y =\pm \sqrt( \frac{2}{3} x^2 -1)$$ which I can easily plot. This is where I have problems. How do I plot the left and right hyperbola? What would I set the function to so as to do this? I apologize for the lack of graphs, I wasn't sure how to plot them to show. If you have questions about what I mean for "left and right" contours, let me know. Thanks!