Question

20. Sketch the level curve of the function f(x, y) that contains the point (5,0).

Answer 1

At the given point,

$f(5,0) = \dfrac1{\sqrt{5^2 + 0^2 - 9}} = \dfrac1{\sqrt{16}} = \dfrac14$

Then the level curve is

$\dfrac1{\sqrt{x^2 + y^2 - 9}} = \dfrac14 \\\\ \implies \sqrt{x^2 + y^2 - 9} = 4 \\\\ \implies x^2 + y^2 - 9 = 4^2 \\\\ \implies x^2 + y^2 = 25 = 5^2$

which is a circle centered at the origin with radius 5 - quite easy to sketch.