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# Orthogonal Trajectory?

find the orthogonal trajectories of the family of curves given by

the equation

y = k / x

where k is an arbitrary constant

Could you please show working:)

Cheers

### 3 Answers

- Anonymous1 decade agoFavorite Answer
I don't know how much this is going to help, but to start, you can base your answer off the fact that this is a direct variation equation. This basically means that with k as a constant, y varies directly with x. In other words, if the constant is positive, you will have a constantly positive slope, but if the constant is negative, you will have a consistently negative slope.

With that said, I'm not sure how much information is needed for the family of curves you want.

- qwertLv 51 decade ago
first find the diff. equation of the given family, then replace y' with (-1/y' ) to get the diff.equation of the orthogonal trajectory, then solve the resultant diff. equation

see this page for more details

- albertinaLv 45 years ago
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