- #1
Bel_Oubli
- 18
- 0
Homework Statement
Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen.
y = x/(1+kx)
2. The attempt at a solution
I have been trying this problem for hours, and I get a different answer every time. I have a big exam over this material tomorrow, and I just discovered that someone in this forum may be able to help me. Any help will be GREATLY appreciated!
The following is my most recent attempt. This was after I got help from a friend. I know that it must be wrong, but it's as far as I have gotten.
y = x/(1+kx)
y' = dy/dx = x/[(x+kx)^2]
slope of tangent line = x/[(x+kx)^2]
slope of orthogonal line = -(1+kx)^2
dy = [-(1+kx)^2]dx
After that, I am completely stuck. I do not think I am anywhere close to the answer. Also, I have no idea how to go about graphing it. Please help!
Last edited: