is an analytic function and
What geometric relationship exists between the level curves of and those of ?
Draw a rough sketch of these level curves for the case to support your answer.
I haven't really any idea where to start this.
What you need to do is plot a few level curves, like and same for . It is easier for : we have (hyperbola). For , if you don't know conics (these are also hyperbola), you can plot the level curves on your calculator or computer (equation (either + or -)), together with level curves for v and see what relation there is between both (you'll need an orthonormal basis to see it).