Consider the following functions$-$

i$)$ f $($x$,$y$)=$xy$.$

ii$)$ f$($x$,$ y$)=$ x$^2-$y$^2$ and iii$)$ f$($x$,$

y$)=$ x$^2+$ y$^2$

a$)$ Sketch a level curve of each of the function.

b$)$ Based on level curve curves or otherwise, draw the graphs of the functions.