Actually this may not be calculus but I am posting it here because its in the Calculus book and is in the curves and arc length etc which sure is calculus...

The question says...

Determine the isotherms of the temperature fields in the plane given by the following scalar functions.

$\displaystyle T = \frac{y}{x^2 + y^2}$

This one

*looks* like a close relative of circle but I can't figure out mathematically...That y is kinda disturbing.

$\displaystyle T = x^2 - Y^2 + 8y$

lost

and lastly

how is $\displaystyle T= xy$ a hyperbola ?