How to get level curve equations

Question

The function is: g(x, y) = x² /(2x − y²) .

Find the equations of the level curves of g at k = −1, 0, 1

Answer 1

Solution

When x=-1

g(x-1,y)=( x-1)'2/2(x-1)-y'2

When x= o

g(0+x,y)=( x+0)'2/2(x+0)-y'2

When x= 1

g(1+x,y)= (1+x)'2/2(x+1)-y'2