Get Answers to all your Questions

header-bg qa

Equation of curve such that length of tangent drawn at its any point is \sqrt2 times ordinate of thet point, will be

  • Option 1)

    y = 2x + c

  • Option 2)

    y = x + c

  • Option 3)

    y = 3x +c

  • Option 4)

    y = 4x +c

 

Answers (1)

best_answer

AS we have learnt,

 

Length of Tangent -

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

- wherein

 

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

On squaring, we get 

y^2\left ( {1+\left (\frac{dx}{dy}{} \right )^{2}} \right ) = 2y^2 \Rightarrow \frac{\mathrm{d} x}{\mathrm{d} y } = 1, -1 \\*\Rightarrow y = x + c \;or\; y =-x + c

 


Option 1)

y = 2x + c

Option 2)

y = x + c

Option 3)

y = 3x +c

Option 4)

y = 4x +c

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE