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]`
`impliesy^(2)-x^(2)=4a^(2)`
On differentating both sides w.r.t. 'x', we get
`2y(dy)/(dx)-2x=0`
`implies2(y(dy)/(dx)-x)=0`
`therefore(dy)/(dx)=(x)/(y)`