Circle And System Of Circles Question 347
Question: The number of common tangents to the circles $ x^{2}+y^{2}-4x-6y-12=0 $ and $ x^{2}+y^{2}+6x+18y+26=0 $ is
[MP PET 1995]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
Centres of circles are $ C_1(2,\ 3) $ and $ C_2(-3,\ -9) $ and their radii are $ r_1=5 $ and $ r_2=8 $ . Obviously $ r_1+r_2=C_1C_2 $ i.e., circles touch each other externally.
Hence there are three common tangents.
BETA
