C1:(x−1)2+(y+9)2=4 C2:(x+4)2+(y−3)2=225 Let's at first solve the equations 10x−24y−278=0 5x−12y−139=0 Let's also check the perpendicular distance from centre of both the circles. From C1:
|5⋅1−12⋅(−9)−139|
13
=
26
13
=2 From C2:
|(5⋅−4)−(−12⋅3)−225|
13
=
195
13
=15 As the perpendicular distance from both the centre of the circles is same as the length of radius. So, this line is only the common tangent. 5x−12y−139=0 5(
−2
5
)−12(
−47
4
)−139=0 Option (d) satisfies the equation, so we can say that (d) is the correct option.