Consider the surface given by the function $f(x,y) = \frac{4}{\sqrt{x^2+y^2-9}}$. Draw the level curves for the values $c = 1$ and $c = 2$. Be sure to label your axes to indicate the scale. Note: When graphing the equation $f(x, y) = c$ here, you will want to rearrange the equation to put it in a recognizable form. Hint: Get the variables out of the denominator and eliminate the radical.
Determine any $y$-intercept(s) of $f$. Write the answer(s) as ordered triples and do not round any of the coordinates.
I was able to find and graph the domain of $f$ and was also able to find the range. However, I'm having a lot of trouble drawing the level curves -- I'm not even sure of the form I should rearrange the equation to. Would someone be able to point me in the right direction?
$\endgroup$1 Answer
$\begingroup$Hint
$$ \frac{4}{\sqrt{x^2+y^2-9}}=c \implies \frac{16}{{x^2+y^2-9}}=c^2\implies x^2+y^2=9+\frac {16}{c^2}$$
Do you recognize something here ?
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