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  • Need clarity, kindly explain! Equation of curve such that subnormal at nay point of it is twice the abcsissa of that point will be

Equation of curve such that subnormal at nay point of it is twice the abcsissa of that point will be

  • Option 1)

    y^2 - 2x = c

  • Option 2)

    y^2 + 2x = c

  • Option 3)

    y^2 + 2x^2 = c

  • Option 4)

    y^2 - 2x^2 = c

 

Answers (1)

best_answer

As we have learnt,

 

Subnormal -

Length =y\tan\alpha = y\frac{dy}{dx}

- wherein

 

 

According to equation -

y\frac{\mathrm{d} y}{\mathrm{d} x} = 2x \Rightarrow ydy- 2xdx = 0

On Integrating, we get - 

\frac{y^2}{2} - x^2 =c\Rightarrow y^2 -2x^2 = 2c\;or\; y^2 -2x^2 = c


Option 1)

y^2 - 2x = c

Option 2)

y^2 + 2x = c

Option 3)

y^2 + 2x^2 = c

Option 4)

y^2 - 2x^2 = c

Posted by

Himanshu

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