# The graphs of f(x, y) = x 2 − y 2 , h(x, y) = xy have been attached.

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.

All the graphs after shifting the k-slider 1 unit have been attached:

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