Question

The orthogonal trajectory of
the series of hyperbolas
xy= c² is

a)x^2+y^2=c^2
b)x^2y^2=c^2
c)y^2-x^2=c^2
d)none​

Answer 1

Answer:none bcoz:

Given curve is

xy = c2 

x(dy/dx) + y = 0

(dy/dx) = -(y/x)

Replacing dy/dx by – dx/dy, we get

-dx/dy = –y/x

xdx – ydy = 0

2xdx – 2ydy = 0

Integrating, we get

  x2 – y2 = a2

which is the required orthogonal trajectories.

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