Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Solve! - Differential equations - JEE Main-6
# Engineering

Given that the slope of the tangent to a curve y=y(x) at any point \left ( x,y \right ) is \frac{2y}{x^{2}}. If the curve passes through the centre of the circle x^{2}+y^{2}-2x-2y=0, then its equation is : 


 

  • Option 1)

    x\log_{e}\left | y \right |=2(x-1)

  • Option 2)

    x\log_{e}\left | y \right |=-2(x-1)

  • Option 3)

    x^{2}\log_{e}\left | y \right |=-2(x-1)

     

  • Option 4)

    x\log_{e}\left | y \right |=x-1

 

Answers (1)
S solutionqc

given slope of tangent =\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{2y}{x^{2}}

\frac{\mathrm{d} y}{\mathrm{y} }=\frac{\mathrm2{dx} }{\mathrm{x} ^{2}}

Integrate but side.

\ln \left ( y \right )=-\frac{2}{x}+C

It passes through centre of circle x^{2}+y^{2}-2x-2y=0  i.e\: \: \left ( 1,1 \right )

0=-2+C\Rightarrow C=2

Eq. of curve is 

x\cdot \ln \left | y \right |=-2+2x

\Rightarrow x\cdot \ln \left | y \right |=2(x-1)


Option 1)

x\log_{e}\left | y \right |=2(x-1)

Option 2)

x\log_{e}\left | y \right |=-2(x-1)

Option 3)

x^{2}\log_{e}\left | y \right |=-2(x-1)

 

Option 4)

x\log_{e}\left | y \right |=x-1

Similar Questions

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions