Question

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

f(x, y) is shown in the picture attached.​

Answer 1

At the given point,

`f(5,0) = \frac1{√(5^2 + 0^2 - 9)} = \frac1{√(16)} = \frac14`

Then the level curve is

`\frac1{√(x^2 + y^2 - 9)} = \frac14 \\\\ \implies √(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.