Question

find the orthogonal trajectories of
y^a = k*x^b..depending on parameter k (a and b are fixed for all curves)..please help!

Answer 1

whats exactly meant by orthogonal trajectories??

Answer 2

an orthogonal trajectory of a family of curves is a curve that intersects each curve at right angles

Answer 3

Implicit differentiate to get\[dy/dx=(bkx ^{b-1})/(ay ^{a-1})\]Integrate both sides to find orthogonal trajectories. Your problem with letters make it treacherous. http://www.nvcc.edu/home/dgoral/291web/ortho.htm