Answer to Question #201768 in Differential Equations for Anuj

Question

Identify the level curves of the following functions:

(i) √(x²+y²)

(ii) √(4 - x² + y²)

(iii) x-y

(iv) x/y

Answer 1

i)

$\sqrt{x^2+y^2}=k$

$x^2+y^2=k^2$

circles with centre at origin and radius k

ii)

$\sqrt{4-x^2+y^2}=k$

$\frac{y^2}{k^2-4}-\frac{x^2}{k^2-4}=1$

hyperbola with asymptotes $y=\pm x$

iii)

$x-y=k$

line with slope 1

iv)

$x/y=k$

$y=x/k$

line with slope $1/k$