$\"\"$

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The equation is $\"\"$ .

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Take reciprocal on both sides.

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$\"\"$

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Diffrentiate on both sides with respective to $\"\"$ .

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Multiply each side by $\"\"$ .

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$\"\"$

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Apply integration :

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$\"\"$

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Let $\"\"$ .

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$\"\"$ .

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$\"\"$

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The function is $\"\"$ .

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(1) Draw the coordinate plane.

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(2) Graph the function $\"\"$ for several values of $\"\"$ .

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$\"\"$ .

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Observe the graph :

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The open curve represents thr given family of curves.

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The closed curves are the orthogonal trajectories.

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$\"\"$

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Graph :

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$\"\"$ .