find the orthogonal trajectories of the family of curves given by
y = k / x
where k is an arbitrary constant
Could you please show working:)
- 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
Hi, just wanted to mention, I loved this discussion. quite inspiring replies