For α , β , z ∈ ℂ and λ > 1 , if λ - 1 is the radius of the circle z - α 2 + z - β 2 = 2 λ , then α - β is equal to _____.

Step-by-step solution

Given, α ,   β ,   z ∈ ℂ and λ > 1 , And λ - 1 is the radius of the circle z - α 2 + z - β 2 = 2 λ Now we know that equation of circle is given by, z - z 1 2 + z - z 2 2 = z 1 - z 2 2 , where radius is given by r = z 1 - z 2 2 , On comparing with z - α 2 + z - β 2 = 2 λ , we get Radius z 1 - z 2 2 = α - β 2 and α - β 2 = 2 λ ⇒ α - β 2 = λ - 1   given ⇒ α - β = 2 λ - 1 &