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  • Answer please! The equation of curves for which subtangent at any point of it is same as sum of co-ordinates of that point is

The equation of curves for which subtangent at any point of it is same as sum of co-ordinates of that point is

  • Option 1)

    x = y\ln y + cy

  • Option 2)

    y = x^2\ln y + cy

  • Option 3)

    y = x\ln y + cy

  • Option 4)

    x^2 = y\ln y + cy

 

Answers (1)

best_answer

As we have learnt,

 

Subtangent -

Length = y_{o}\cot \alpha = y\frac{dx}{dy}

- wherein

 

 According to the given condition

y\frac{\mathrm{d} x}{\mathrm{d} y} = x + y \Rightarrow ydx = xdy + ydy

Dividing by y^2, on both sides we get -

\\*\Rightarrow \frac{ydx-xdy}{y^2} = \frac{dy}{y} \Rightarrow d\left(\frac{x}{y} \right ) = \frac{dy}{y}

On integrating, we get

\frac{x}{y} = \ln y + c \Rightarrow x = y\ln y + cy


Option 1)

x = y\ln y + cy

Option 2)

y = x^2\ln y + cy

Option 3)

y = x\ln y + cy

Option 4)

x^2 = y\ln y + cy

Posted by

Himanshu

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