Form Differentiate Equation Circles Which Pass Through Origin And Whose Centres Lie Axis

Form the differentiate equation of all circles which pass through origin and whose centres lie on y – axis.


It is given that circles pass through origin and their centres lie on y-axis.
Let (0,k) be the centre of the circle and radiud is k.
So, the equation of circle is
(x-0)2 + (y-k)2 = k2
⇒ x2 + y2 – 2ky = 0 ….(i)
Differentiating w.r.t.x, we get