The number of common tangent to the circles x2+y2-4x-6y-12=0 and x2+y2+6x+18y+26 = 0 is
-
1
-
2
-
3
-
4
C.
3
Number of common tangents depend on the position of the circle with respect to the each other.
(i) If circles touch externally ⇒C1C2 = r1+ r2,3 common tangents
(ii) If circles touch internally ⇒ C1C2 = r2-r1, 1 common tangents
(iii) If circles do not touch each other, 4 common tangents
Given equations of circles are
x2 +y2-4x-6y-12 = 0 .. (i)
x2+y2+6x+18y+26 =0 ... (ii)
Centre of circle (i) is C1 (2,3) and radius
=
Centre of circle (ii) is C2(-3,-9) and radius
Thus, both circles touch each other externally. Hence, there are three common tangents.