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

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

Steve · Answer

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.