Question

Given the function f(x,y)=y/(x^2+y^2), give and identify the level curves for k=1, k=1/2, and k=1/4, and draw a contour map showing these level curves. Any help would be immensely appreciated. Thanks
Just set y/(x^2 + y^2) = k
y = kx^2 + ky^2
x^2 + y^2 - y/k = 0
x^2 + (y - 1/2k)^2 = 1/4k^2

That is a circle with center at (0,1/2k) with diameter 1/k.

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