The differential equation of the family of circles passing through the points 0 , 2 and 0 , - 2 is

Step-by-step solution

Given a circle passing through 0 , - 2 and 0 , 2 , so its equation will be, x - x 1 x - x 2 + y - y 1 y - y 2 + λ 1 x y 1 x 1 y 1 1 x 2 y 2 1 = 0 , λ 1 ∈ R On putting the given values we get, ⇒ x - 0 x - 0 + y - 2 y + 2 + λ 1 x y 1 0 2 1 0 - 2 1 = 0 , λ 1 ∈ R ⇒ x 2 + y 2 - 4 + λ 1 4 x = 0 ⇒ x 2 + y 2 - 4 + λ x = 0 , λ ∈ R Now dividing both side by x we get, ⇒ x 2 + y 2 - 4 x + λ = 0 Now differentiating with respect to x ⇒ x 2 x