If the variable line 3 x + 4 y = α lies between the two circles ( x - 1 ) 2 + ( y - 1 ) 2 = 1 and ( x - 9 ) 2 + ( y - 1 ) 2 = 4 , without intercepting a chord on either circle, then the sum of all the integral values of α is

Step-by-step solution

Given line 3 x   +   4 y   =   α Given circles ( x - 1 ) 2 + ( y - 1 ) 2 = 1   &   ( x - 9 ) 2 + ( y - 1 ) 2 = 4 According to the given information centres of both the circles must lie on opposite side of line. L 11   .   L 22   <   0 ⇒   3   + 4   - α   27   +   4   -   α   < 0 α   ∈   7 ,   31   . Line is neither touching nor intersecting that means perpend