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Question
If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
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Solution
`x=a(t-1/t),y=a(t+1/t)`
`x/a=t-1/t and y/a=t+1/t`
we have
`(t+1/t)^2=(t-1/t)^2+4`
`(y/a)^2=(x/a)^2+4`
`y^2/a^2-x^2/a^2=4`
`y^2-x^2=4a^2`
Differentiating w.r.t. x
`2y dy/dx-2x=0`
`dy/dx=2x/2y`
`dy/dx=x/y`
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