find the orthogonal trajectories of the family of curves x^2+y^2=2gxwhere g is arbitary constant
find the orthogonal trajectories of the family of curves x^2+y^2=2gx
where g is arbitary constant
Raj , 6 Years ago
Grade 12
Integral Calculus> find the orthogonal trajectories of the f...
1 AnswersVikas TU
Dear student
x^2+y^2=2gx .......(1)
Differentiate wrt x
2x + 2ydy/dx = 2g
Find the value of g from here and put it to equation 1
x^2+y^2= x (x + ydy/dx)
Replace dy/dx with -dx /dy
(y^2 - x^2 )/ xy = -dx /dy
Put x = ty
dx /dy = dt/dy *y + t
put in place of dx /dy
inegral (2t/(1+t^2) dt = -(integral (dy/y))
ln(1+t^2) = -lny + lnK
Final ans is
x^2 + y^2 = ky
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