Suppose the family of lines a x + b y + c = 0 (where a , b , c are in arithmetic progression) be normal to a family of circles. The radius of the circle of the family which intersects the circle x 2 + y 2 - 4 x - 4 y - 1 = 0 orthogonally is

Step-by-step solution

Since, a , b , c are in A . P a x + b y + c = 0 represents a family of lines passing through the point 1 , - 2 . So, the family of circles (concentric) will be given by x 2 + y 2 - 2 x + 4 y + c = 0 and 2 - 1 × - 2 + 2 × - 2 = - 1 + c ⇒ c = - 3 ⇒ radius = 1 + 4 + 3 = 2 2 units