Total number of lines touching atleast two circles of the family of four circles x 2 + y 2 ± 3 x ± 8 y = 0 is

Step-by-step solution

Let, C 1 be circle x 2 + y 2 + 8 x + 8 y = 0 , C 2 be circle x 2 + y 2 + 8 x - 8 y = 0 , C 3 be circle x 2 + y 2 - 8 x + 8 y = 0 & C 4 be circle x 2 + y 2 - 8 x + 8 y = 0 Now, common tangents between C 1   &   C 2 is 2 , common tangents between C 1   &   C 3 is 2 , common tangents between C 1   &   C 4 is 3 , common tangents between C 2   &   C 3 is 3 , common tangent between C 2   &   C 4 is 2 & common tangent between C 3   &   C 4