Which of the following is not the differential equation of family of curves whose tangent from an angle of `pi/4` with the hyperbola `xy=c^(2)`?

Options

A. `(dy)/(dx)=(x-y)/(x+y)`
B. `(dy)/(dx) = x/(x-y)`
C. `(dy)/(dx) = (x+y)/(y-x)`
D. None of these

Answer

B

Explanation

`xy=C`
or `x(dy)/(dx)+y=0`
or `(dy)/(dx)=-y/x=m_(1)`
By condition,
`tanpi/4=|(m_(1)-m_(2))/(1+m_(1)m_(2))|`
`1=|(-y/x-m_(2))/(1-y/xm_(2))|`
or `y/x+m_(2)=1-y/xm_(2)` or `y/xm_(2)-1`
or `(dy)/(dx) = (x-y)/(x+y)` or `(dy)/(dx) = (x+y)/(y-x)`