Question

The number of common tangents that can be drawn to the circle $x^2+y^2–4x–6y–3=0$ 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 $3$

The two circles are

$x^2+y^2–4x–6y–3=0$ and $x^2+y^2+2x+2y+1=0$

Centre:$C_1=(2,3)$

$C_2=(–1,–1)$

radii : $r_1=4,r_2=1$

We have $C_1{C}_2=5=r_1+r_2,$

$\therefore$ there are $3$ common tangents to the given circles.