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If x=a(t-(1)/(t)),y=a(t+(1)/(t)),"show t...

If `x=a(t-(1)/(t)),y=a(t+(1)/(t)),"show that "(dy)/(dx)=(x)/(y)`

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AI Generated Solution

To show that \(\frac{dy}{dx} = \frac{x}{y}\) given the equations \(x = a\left(t - \frac{1}{t}\right)\) and \(y = a\left(t + \frac{1}{t}\right)\), we will follow these steps: ### Step 1: Express \(x\) and \(y\) in terms of \(t\) Given: \[ x = a\left(t - \frac{1}{t}\right) \] \[ ...
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Knowledge Check

  • If x=(t+1)/(t),y=(t-1)/(t)," then "(dy)/(dx)=

    A
    1
    B
    0
    C
    2
    D
    `-1`

  • If x=t^(2)+(1)/(t^(2)),y=t-(1)/(t)," then "(dy)/(dx)=

    A
    `(1)/(1+t^(2))`
    B
    `(1)/(t^(2)-1)`
    C
    `(1)/(1-t^(2))`
    D
    `(1)/(2y)`

  • If x=(2t)/(1+t^(2)),y=(1-t^(2))/(1+t^(2))," then "(dy)/(dx)=

    A
    `(2t)/(t^(2)-1)`
    B
    `(2t)/(t^(2)+1)`
    C
    `(2t)/(1-t^(2))`
    D
    `-1`

    • Similar Questions

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    If x=acos^(3)t,y=asin^(3)t,"show that "(dy)/(dx)=-((y)/(x))^((1)/(3))

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