The number of common tangents, to the circles x 2 + y 2 - 18 x - 15 y + 131 = 0 and x 2 + y 2 - 6 x - 6 y - 7 = 0 , is

Step-by-step solution

If S ≡ x 2 + y 2 + 2 g x + 2 f y + c = 0 . C ≡ - g , - f and r = g 2 + f 2 - c . The given circles are x 2 + y 2 - 18 x - 15 y + 131 = 0 ⇒ C 1 9 ,   15 2 ,   r 1 = 81 + 225 4 - 131 = 5 2 and x 2 + y 2 - 6 x - 6 y - 7 = 0 ⇒ C 2 3 ,   3 ,   r 2 = 9 + 9 + 7 = 5 ⇒ d = C 1 C 2 = 9 - 3 2 + 15 2 - 3 2 = 36 + 81 4 = 15 2 ⇒ r 1 + r 2 = 5 2 + 5 = 15 2 ⇒ C 1 C 2 = r 1 + r 2 ∴ Circles touch each other externally, 3 common tangents. Hence this is the correct op