Find two level curves of the function #f(x,y)=(x+y)/(x-y),x≠y# and sketch them?

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Answer 1 · 2018-02-15T17:13:11

See below.

A level curve is the set of points such that

#f(x,y) = C_1# then

#x+y = C_1(x-y) rArr y = ((C_1-1)/(C_1+1))x#

Now taking two values for #C_1 ne -1# we will get the two level curves.

Attached a plot showing the level curves for

#C_1 = -2# blue
#C_1 = 0# green
#C_1 = 2# red

enter image source here