   Chapter 2.6, Problem 54E

Chapter
Section
Textbook Problem

# Find the value of the number a such that the families of curves y = ( x +   c ) − 1 and y = a ( x + k ) 1 / 3 are orthogonal trajectories.

To determine

To find:

The value of number a

Explanation

1) Given:

y=x+c-1 andy=ax+k1/3 a re orthogonal trajectories

2) Calculation:

y=x+c-1=1x+cx+c=1y

Differentiating x+c=1y implicitly with respect to x we get,

1+0=-1y2dydx

dydx=-y2

Now consider,

y=ax+k1/3

y3=a3(x+k)

y3=a3

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