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If the ellipse $\frac{x^{2}}{4} + y^{2} = 1$ meets the ellipse $x^{2} + \frac{y^{2}}{a^{2}} = 1 (a \in R)$ in four distinct points and $a = b^{2} - 3 b - 9$ , then total number of integers which are not in the solution set of b is_________

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answer is 2.

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Detailed Solution

These two ellipses meet in four distinct point for $a > 1$
$(b + 2) (b - 5) > 0$ so $b \notin {- 2, - 1, 0, 1, 2, 3, 4, 5}$

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