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Question

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:

































1.png
10.png
11.png
2.png
3.png
4.png
5.png
6.png
7.png
8.png
9.png

Step-by-step answer

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Subject: Calculus, Math

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