Question

The number of common tangents to the circles $x^2+y^2-4x-6y-3=0$ and $x^2+y^2+2x+2y+1=0$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Given circles are
$x^2+y^2-4x-6y-3=0$ and $x^2+y^2+2x+2y+1=0$
The centre and radius are
$C_1=(2,3),r_1=\sqrt{4+9+3}=4C_2=(-1,-1),r_2=\sqrt{1+1-1}=1$

Now,
$C_1{C}_2=\sqrt{3^2+4^2}=5r_1+r_2=5\Rightarrow C_1{C}_2=r_1+r_2$

Therefore there are $3$ common tangents to the given circles.