Maharashtra State BoardHSC Arts 12th Board Exam
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If x=a(t-1/t),y=a(t+1/t), then show that dy/dx=x/y - Mathematics and Statistics

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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`

Concept: Derivatives of Functions in Parametric Forms
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