Find the Orthogonal Trajectories of the Family of Curves $x ^ { 2 } + y ^ { 2 } = k$

question 73

Essay

Find the orthogonal trajectories of the family of curves $x ^ { 2 } + y ^ { 2 } = k$ . Then draw several members of each family on the same coordinate plane.

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Definitions:

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A philosopher, economist, and revolutionary from the 19th century, famously recognized for his ideas on capitalism and communism.

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