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Question

# Match the pairs of functions with the given contour diagrams. Which contours represent f and which represent g? (The x - and y-scales are equal.)$f(x, y)=x^2-y^2, g(x, y)=x y$

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Answered 2 years ago
Answered 2 years ago
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The contour $f$ at level $c$ has equation,

\begin{aligned}x^2 - y^2 &= c\\ y^2&=x^2-c\\ y&=\pm\sqrt{\smash[b]{x^2-c}}\end{aligned}

Here, $f$ is shown as hyperbolas.

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