Q90 / 160 · TS EAMCET 2023 (12 May Shift 2) · Mathematics
The number of common tangents to the circles $x^2+y^2-2 x-6 y+9=0$ and $x^2+y^2+6 x-2 y+1=0$ is
- A$1$
- B$2$
- C$3$
- Correct answerD$4$
Solution
$$
S_1: x^2+y^2-2 x-6 y+9=0
$$
Centre $C_1:(1,3)$
Radius $\eta_1=\sqrt{1+9-9}=1$
$$
S_2: x^2+y^2+6 x-2 y+1=0
$$
Centre $C_2:(-3,1)$
Radius $r_2=\sqrt{9+1-1}=3$
$$
\begin{aligned}
& C_1 C_2=\sqrt{(1+3)^2+(3-1)^2}=2 \sqrt{5} \\
& \Rightarrow r_1+r_2=4 \\
& \Rightarrow C_1 C_2>r_1+r_2
\end{aligned}
$$
$\therefore \quad$ Circles are not intersecting and outside each other.
$\therefore \quad$ Number of tangents $=4$.
Hence, the correct answer is option: 'D'.