Question

The length of the greatest common tangent to the circles given by $S_1\equiv x^2+y^2-4=0$ and $S_2\equiv x^2+y^2-12x+27=0$, is

• A. $\sqrt{35}$
• B. $\sqrt{11}$
• C. $\sqrt{5}$
• D. $\sqrt{27}$

Answer 1

The correct option is A $\sqrt{35}$

Given circles
$S_1\equiv x^2+y^2-4=0$
$C_1(0,0),r_1=2$
$S_2\equiv x^2+y^2-12x+27=0$
$C_2(6,0),r_2=3$
Length of common tangent $=\sqrt{(C_1{C}_2{)}^2-(r_1-r_2{)}^2}=\sqrt{36-1}=\sqrt{35}$