question_answer

The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] and \[{{x}^{2}}+{{y}^{2}}+6y+18y+26=0,\] is [JEE Main Solved Paper-2015 ]

A) 3

B) 4

C) 1                                             

D) 2

Correct Answer: A

Solution :

\[{{C}_{1}}=(2,3),{{r}_{1}}=5\] \[{{C}_{2}}=(-3,-9),{{r}_{2}}=8\] \[{{C}_{1}}{{C}_{2}}=13,{{r}_{1}}+{{r}_{2}}=13\] \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\] Circles Touches Extermally