Question

Give an example of a function f(x, y) that is defined on R2 and has only...

Give an example of a function f(x, y) that is defined on R2 and has only hyperbolas as its level sets.

At the moment I have x2 - y2 = k (where k is a constant) as my answer. But I'm not sure if that is correct. It seems to work except when k = 0, which I'll have only two lines (y = x and y = -x) so I'm not too sure what should I do with it. Plus how should I explain that the function is what the question's asking for? What I've done so far was only sketch it when k = 1,2,3,-1,-2,-3 to show they are in the shapes of hyperbolas (and I didn't sketch k = 0 yet). Would that be enough or should I put more work?

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Answer #1

The Example enboie que emough ou is VNL perbolas Sinii red di Here k--3 k--2 k--3

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