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The curve equations are and .
Two curves are said to be orthogonal trajectories when the slopes of the tangent line to both the curves is equal to .
Consider .
Apply derivative on each side with respect to .
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Consider .
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Now, .
Apply derivative on each side with respect to .
Substitute in the above expression.
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Now we can observe that product slope of and is equal to .
Therefore both the curves are orthogonal to each side.
Graph both the curves.
Consider different values of , and .
Graph each curve for different values of , and .
The two curves and are orthogonal to each other.
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