Question

Find the number of common tangents to the circles $x^2+y^2=1$ and $x^2+y^2-2x-6y+6=0$

• A. $4$
• B. $3$
• C. $2$
• D. No common tangent

Answer 1

The correct option is A $4$

Let given Circle,

$S_1:x^2+y^2=1$ and$x^2+y^2-2x-6y+6=0$

The center and radii are

$C_1(0,0)$ and $r_1=1$

$C_2(1,3)$ and $r_2=2.$

$C_1{C}_2=\sqrt{1}0$ and $r_1+r_2=3$

Since, $C_1{C}_2>r_1+r_2$

Therefore. circles don't intersect and they have $4$ common tangents.
Ans: A