If the equation of two circles are $x^{2} + y^{2} + 2 x = 0$ and $(x - 3)^{2} + y^{2} = 9$ , then the number of common tangents is

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Solution

The correct option is D $3$
$S_{1} : x^{2} + y^{2} + 2 x = 0$
Centre, $C_{1} \equiv (- 1, 0)$ , radius, $r_{1} \equiv 1$
$S_{2} : (x - 3)^{2} + y^{2} = 9$
Centre, $C_{2} \equiv (3, 0)$ , radius, $r_{2} \equiv 3$

$C_{1} C_{2} = 4$ and $r_{1} + r_{2} = 4$
$∴ r_{1} + r_{2} = 4 = C_{1} C_{2}$
So, these two circles touch each other externally.
$∴$ Number of common tangents is $3$

Hence, option D.

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