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x = t + (1)/(t), y = t - 1/t...

`x = t + (1)/(t), y = t - 1/t`

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`:' x =t + 1/t` and `y = t - (1)/(t)`
`:. (dx)/(dt)= (d)/(dt)(t+1/t)` and `(dy)/(dt)=(d)/(dt)(t-(1)/(t))`
`rArr (dx)/(dt)=1+(-1)t^(-2)`and ` (dy)/(dt)=1-(-1)t^(-2)`
`rArr (dx)/(dt) =1-1/(t^(2))` and `(dy)/(dt)=1+(1)/(t^(2))`
`rArr (dx)/(dt) = (t^(2)- 1)/(t^(2))` and `(dy)/(dt) = (t^(2)+1)/(t^(2))`
`:.(dy)/(dx) = (dy//dt)/(dx//dt) = (t^(2)+1//t^(2))/(t^(2)-1//t^(2)) = (t^(2)+1)/(t^(2) - 1)`
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