Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Solve! the x-intercept of the tangent to a curve is equal to the ordinate of point of contact. Equation of such curve which pan through (1, 1) is

the x-intercept of the tangent to a curve is equal to the ordinate of point of contact. Equation of such curve which pan through (1, 1) is

 

  • Option 1)

    y\cdot e^{\frac{x}{y}} = e

  • Option 2)

    x\cdot e^{\frac{x}{y}} = e

  • Option 3)

    x\cdot e^{\frac{y}{x}} = e

  • Option 4)

    y\cdot e^{\frac{y}{x}} = e

 

Answers (1)

best_answer

As we have learnt,

 

Length of x - intercept cut by tangent at P(x,y) -

x-y\frac{dx}{dy}

-

 

 According to question -

x-y\frac{dx}{dy} = y \Rightarrow xdy-ydx = ydy \\*\frac{xdy-ydx}{y^2} = \frac{dy}{y} \\* - d\left(\frac{x}{y} \right ) = \frac{dy}{y} \Rightarrow -\frac{x}{y} = \ln y + c \\*\Rightarrow \ln y = -\frac{x}{y} - c \Rightarrow y = e^{-\frac{x}{y} - c} \\*\Rightarrow y = e^{-\frac{x}{y}}\cdot e^{- c} \Rightarrow y = ce^{-\frac{x}{y}} \\* \Rightarrow y\cdot e^{\frac{x}{y}} = c

But Since its passes through (1,1), So c = e

\Rightarrow y\cdot e^{\frac{x}{y}} = e


Option 1)

y\cdot e^{\frac{x}{y}} = e

Option 2)

x\cdot e^{\frac{x}{y}} = e

Option 3)

x\cdot e^{\frac{y}{x}} = e

Option 4)

y\cdot e^{\frac{y}{x}} = e

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question