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  • Can someone explain The equation of curves such that, subtangent at any point of it is same as abscissa is

The equation of curves such that, subtangent at any point of it is same as abscissa is

  • Option 1)

    y = cx^2

  • Option 2)

    y^2 = cx

  • Option 3)

    y =cx

  • Option 4)

    y =x + c

 

Answers (1)

best_answer

As we have learnt,

 

Subtangent -

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

- wherein

 

 According to given condition -

y\frac{\mathrm{d} y}{\mathrm{d} x} = x \Rightarrow \frac{dy}{y} -\frac{dx}{x} = 0

On integrating, we get -

\ln y -\ln x = c\Rightarrow \ln \left(\frac{y}{x} \right ) = c \Rightarrow \frac{y}{x} = e^c \Rightarrow y =cx

 


Option 1)

y = cx^2

Option 2)

y^2 = cx

Option 3)

y =cx

Option 4)

y =x + c

Posted by

Himanshu

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