Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Form the differential equation of the family of circles touching the y-axis at origin.

6.    Form the differential equation of the family of circles touching the y-axis at origin.

Answers (1)

best_answer


If the circle touches y-axis at the origin then the centre of the circle  lies at the x-axis 
Let r be the radius of the circle
Then, the equation of a circle with centre at (r,0) is
(x-r)^2+(y-0)^2 = r^2
x^2+r^2-2xr+y^2=r^2\\ x^2+y^2-2xr=0    -(i)
Now, differentiate w.r.t x
2x+2y\frac{dy}{dx}-2r=0\\ y\frac{dy}{dx}\Rightarrow yy^{'}+x-r=0
yy^{'}+x=r    -(ii)
Put equation (ii) in equation (i)
 x^2+y^2=2x(yy^{'}+x)\\ y^2=2xyy^{'}+x^2
Therefore, the required equation is   y^2=2xyy^{'}+x^2

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question