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  4. The number of common tangents to the circles x2 + y2 = 4, x2 + y2 - 4x + 2y - 4 = 0 is

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Q. The number of common tangents to the circles $x^2 + y^2 = 4, x^2 + y^2 - 4x + 2y - 4 = 0$ is

COMEDKCOMEDK 2014Conic Sections

Solution:

$c_1 = (0, 0), c_2 = (2, -1), r_1 = 2$ and $r_2 = 3 $
$|c_1 c_2| = \sqrt{5}$
$r_1 + r_2 > |c_1 c_2|$
So, there are two common tangents