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.

Answers:

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