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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.5, Problem 43E

To determine

**To show:** One family of the curves are orthogonal trajectories to the other family.

Expert Solution

**Given:**

The curves

**Derivative rules:**

*Chain rule*:

**Proof:**

Obtain the slope of the curves

Thus the slope of the tangent to the curve

Obtain the slope of the curves

Thus, the slope of the equation

The product slope is computed as follows,

If

If

Substitute the value

The line

Therefore, the curves

**Graph:**

The family of the curves

From the graph, it is observed that the family of the curves