The line x = y touches a circle at the point ( 1 , 1 ) . If the circle also passes through the point ( 1 , - 3 ) , then its radius is

Step-by-step solution

Equation of family of circles touches line x – y = 0 at point ( 1,1 ) is ( x - 1 ) 2 + ( y - 1 ) 2 + λ x – y = 0 ,   λ ∈ R If a member of this family, also passes through point ( 1 , – 3 ) then 1 - 1 2 + - 3 - 1 2 + λ 1 - - 3 = 0 ⇒ λ = - 4 ⇒   Required circle is x - 1 2 + y - 1 2 - 4 x - y = 0 ⇒ x 2 + y 2 - 6 x + 2 y + 2 = 0 Where radius is r = 3 2 + 1 2 - 2 = 2 2