The graph of f(x, y) = x 2 y 2 , h(x, y) = xy. Use the slider k to study some of the level curves of f and use the slider m to study some of the level curves of h. Based on your observation make a conjecture whether the level curves of f and h are orthogonal to each other for all (x, y) 6= (0, 0). Try to prove your conjecture.

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