A circle passes through the points 2 , 3 and 4 , 5 . If its centre lies on the line y - 4 x + 3 = 0 , then its radius is equal to :

Step-by-step solution

Let centre of circle be C α ,   β . It lies in line y - 4 x + 3 - 0 ⇒ β = 4 α - 3 ∴   C   α ,   4 α - 3 ∴ C A = C B By distance formula, ⇒ α - 2 2 + 4 α - 6 2 = α - 4 2 + 4 α - 8 2 ⇒ - 4 α + 4 - 48 α + 36 = - 8 α + 16 - 64 α + 64 ⇒ 64 + 8 - 4 - 48 α = 80 - 40 ⇒ α = 40 20 = 2 ∴   C 2 , 5 ∴   r = 2 - 2 2 + 5 - 3 2 = 2