Question

The number of common tangents to the circles $x^2+y^2-2x-4y+1=0$ and $x^2+y^2-12x-16y+91=0$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$C_1\equiv (1,2)$ $r_1=\sqrt{1+4-1}=2$
$C_2\equiv (6,8)$ $r_2=\sqrt{36+64-91}=3$
$C_1{C}_2=\sqrt{25+36}=\sqrt{61}$
$R_1+r_2=5<\sqrt{61}$
Circle are far apart

$\therefore$ no of common tangents $=4$