Exp. (c)Central Idea Number of common tangents depend on the position of the circle with respect to each other.(i) If circles touch externally ⇒C1​C2​=r1​+r2​,3 common tangents(ii) If circles touch internally ⇒C1​C2​=r2​−r1​,1 common tangent(iii) If circles do not touch each other, 4 common tangentsGiven equations of circles arex2+y2−4x−6y−12=0.....(i) and x2+y2+6x+18y+26=0.....(ii) Centre of circle (i) is C1​(2,3) and radius =4+9+12​=5(r1​) Centre of circle (ii) is C2​(−3,−9) and radius=9+81−26​=8(r2​), (say)Now, C1​C2​=(2+3)2+(3+9)2​⇒⇒​C1​C2​=52+122​C1​C2​=25+144​=13​∴ Also, ​r1​+r2​=5+8=13C1​C2​=r1​+r2​​Thus, both circles touch each other externally.Hence, there are three common tangents.