If `x=a(t-(1)/(t)),y=a(t+(1)/(t))`, where t be the parameter, then `(dy)/(dx)=?`

Options

A. `y/x`
B. `(-x)/(y)`
C. `x/y`
D. `(-y)/(x)`

Answer

C

Explanation

Given , `x = a(t-1/t)` and `y = a (t+1/t)`
Now, `y^(2) - x^(2) =a^(2) [(t+1/t)^(2) - a^(2) (t-1/t)^(2)]`
`= a^(2) [t^(2) +1/(t^(2)) + 2 - t^(2) - 1/(t^(2)) + 2 ]`
`rArr y^(2) - x^(2)= 4a^(2)`
On differentiating both sides w.r.t. `'x'`, we get
`2y '(dy)/(dx) - 2x = 0`
`rArr 2(y '(dy)/(dx) - x) = 0`
`:. (dy)/(dx) = x/y`