Asked by TayB
Find the orthogonal trajectories for the family of curves y=(kx)^6.
Answers
Answered by
Steve
for our function,
y' = 6k(kx)^5
so, we want other curves whose slope is
y' = -1/(6k^6) x^-5
y = 1/(24k^6 x^4)
or, to make things look more similar,
y = 1/(24k^2) (kx)^-4
y' = 6k(kx)^5
so, we want other curves whose slope is
y' = -1/(6k^6) x^-5
y = 1/(24k^6 x^4)
or, to make things look more similar,
y = 1/(24k^2) (kx)^-4
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