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  • How to solve this problem- Equation of curve passing through (2,2) such that subtangent and subnormal at any point of it are equal is

Equation of curve passing through (2,2) such that subtangent and subnormal at any point of it are equal is

  • Option 1)

    y = -x

  • Option 2)

    y + x =2

  • Option 3)

    y = x

  • Option 4)

    y + x =3

 

Answers (1)

best_answer

As we have learnt,

 

Subnormal -

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

- wherein

 

 Subnormal= y\frac{\mathrm{d} y}{\mathrm{d} x} and subtangent = y\frac{\mathrm{d} x}{\mathrm{d} y}

According to question -

y\frac{\mathrm{d} x}{\mathrm{d} y} = y\frac{\mathrm{d} y}{\mathrm{d} x}\Rightarrow\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right)^2= 1

\\*\Rightarrow \frac{\mathrm{d} y}{\mathrm{d} x} = 1 \; or\; -1 \\*\Rightarrow y = x+ c\;or\; y = -x + c \\*\Rightarrow x-y = c\;or\;x+y = c

But the curve passes through (2,2) so they must satisfy hence, curves are either y = x or x+ y = 4

 


Option 1)

y = -x

Option 2)

y + x =2

Option 3)

y = x

Option 4)

y + x =3

Posted by

Himanshu

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