The points of intersection of the line a x + b y = 0 , ( a ≠ b ) and the circle x 2 + y 2 - 2 x = 0 are A ( α , 0 ) and B ( 1 , β ) . The image of the circle with A B as a diameter in the line x + y + 2 = 0 is :

Step-by-step solution

Given, The points of intersection of the line a x + b y = 0 , ( a ≠ b ) and the circle x 2 + y 2 - 2 x = 0 are A α , 0 and B ( 1 , β ) then, For point A α , 0 a ( α ) + b ( 0 ) = 0 ⇒ α = 0 And, α 2 - 2 α = 0 ⇒ α = 0 , 2 For point B ( 1 , β ) a + b β = 0 Or, β = - b a And, 1 + β 2 - 2 = 0 ⇒ β = ± 1 ∵ a ≠ b therefore, Only possibility α = 0 ,   β = 1 Points are A 0 , 0 and B 1 , 1 So the centre of