If the circles x 2 + y 2 - 10 x + 16 y + 89 - r 2 = 0 and x 2 + y 2 + 6 x - 14 y + 42 = 0 have common points, then the number of possible integral values of r is equal to

Step-by-step solution

Centre & radius of x 2 + y 2 - 10 x + 16 y + 89 - r 2 = 0 are 5 , - 8 & r respectively Centre & radius of x 2 + y 2 + 6 x - 14 y + 42 = 0 are - 3,7 & 4 respectively Distance between the centres of circles is 8 2 + 1 5 2 = 17 ⇒ 17 - 4 ≤ r ≤ 17 + 4 ⇒ 13 ≤ r ≤ 21 ⇒ r ∈ ± 21 , ± 20 , ± 19 , ± 18 , ± 17 , ± 16 , ± 15 , ± 14 , ± 13 Hence, the number of possible values of r is equal to 18