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If $a, b \in {- 10, - 9, .....9, 10}$ and common tangents of the circles $x^{2} + y^{2} + 2 a x = 0$ and $x^{2} + y^{2} + 2 b x = 0$ form an equilateral triangle, then number of possible ordered pairs (a,b) is _____

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answer is C.

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Detailed Solution

$\begin{array}{l} a b < 0 \\ a n d | a | = 3 | b | \\ (o r) | b | = 3 | a | \end{array}$

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