Orthogonal Trajectories

• Oct 24th 2009, 09:30 AM
Cursed
Orthogonal Trajectories
I'm confused as to how to do orthogonal trajectory problems. The current calculus book I have doesn't explain how to do these problems, yet these problems appear in the back of some of the chapters in the book.

Here's an example 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.

How would I go about doing this?
• Oct 24th 2009, 07:59 PM
TKHunny
Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

Let's see what you get.
• Oct 24th 2009, 08:37 PM
tonio
Quote:

Originally Posted by TKHunny
Orthogonal trajectories are families of curves that intersect at right angles. This must mean that the product of their respective derivatives is -1.

Let's see what you get.

I think it must be "...the product of their respective derivatives at their intersection point is -1"

Tonio
• Oct 24th 2009, 08:50 PM
Arturo_026
One related question:
Since they're orthogonal then it means that y' of the first is (m) and y' of the other is (-1/m) at their point of intersection right?
• Oct 24th 2009, 09:28 PM
TKHunny
Well, for m NOT = zero (0), m*(-1/m) = -1