Question

The number of common tangents of the circles $x^2+y^2-2x-1=0$ and $x^2+y^2-2y-7=0$

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

$1$

Let $S_1:x^2+y^2-2x-1=0$ and $S_2:x^2+y^2-2y-7=0$
$\Rightarrow C_1=(1,0),r_1=\sqrt{1+1}=\sqrt{2},C_2=(0,1),r_2=\sqrt{1+7}=2\sqrt{2}$
Now $C_1{C}_2=\sqrt{1+1}=\sqrt{2}$. Clearly $C_1{C}_2=r_2-r_1$
Therefore circle $S_1$ touches $S_2$ internally.Thus there will exist only one common tangent.