Q. 105.0( 1 Vote )

Find the differential equation of all the circles which pass through the origin and whose centers lie on the x - axis.

Answer :

Any circle with centre at (h, k) and radius r is given by,

(x – h)2 + (y – k)2 = r2


Here centre is on x - axis, so k = 0


So, we have the equation of circle as, (x – h)2 + y2 = r2


Further it is given that circle passes through origin (0,0) therefore origin must satisfy equation of circle. So, we get,


0 + h2 = r2


So, the equation of circle is (x – h)2 + y2 = h2


x2 – 2hx + y2 = 0


x2 + y2 = 2hx



Now, differentiating it with respect to x we get,






Hence, the required differential equation is


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on DIfferential CalculusFREE Class
Functional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses