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Problem

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Textbook Expert
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24 Oct 2021

Given information

Given the curves are .

The main objective is to show that the given families of curves are orthogonal trajectories of each other, that is, every curve in one family is orthogonal to every curve in the other family. Sketch both families of curves on the same axes.

Step-by-step explanation

Step 1.

Use the implicity differentiation to find the derivatives of two functions .

Differentiate   with respect to :

 

So, the slope of the tangent line of the curve is               ...... (1)

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