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  • Give answer! Equation of curves such that tangent and normal drawn at any point of which are of equal length, is

Equation of curves such that tangent and normal drawn at any point of which are of equal length, is

  • Option 1)

    y =3x +c

  • Option 2)

    y =2x +c

  • Option 3)

    y =4x +c

  • Option 4)

    y =x +c

 

Answers (1)

best_answer

As we have learnt,

 

Length of Normal -

y\sqrt{1+\left ( \frac{dy}{dx} \right )^{2}}

- wherein

 

 

y\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}}=y\sqrt{1+\left ( \frac{dy}{dx} \right )^{2}}

Squaring both sides we have 

\left(\frac{dx}{dy} \right )^{2}=\left ( \frac{dy}{dx} \right )^{2} \\*\Rightarrow \frac{dx}{dy} = \pm \frac{dy}{dx} \\*\Rightarrow \frac{dy}{dx} = 1 \; or\;-1

\therefore Curves are either  y = x + c \;or\; y = -x + c


Option 1)

y =3x +c

Option 2)

y =2x +c

Option 3)

y =4x +c

Option 4)

y =x +c

Posted by

Himanshu

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