$\"\"$

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The equation is $\"\"$ .

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Diffrentiate 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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Seperate the variables.

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$\"\"$

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Now integrate on both sides.

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$\"\"$

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Where $\"\"$ is an integration constant.

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$\"\"$ .

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Substiute $\"\"$ .

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$\"\"$ .

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From the logarthamic property : $\"\"$ and $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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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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The circles represents the given family of curves.

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The curves represents the orthoganal trajectories.

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$\"\"$

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Graph :

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$\"\"$