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# If the curve x^{2} + 3y^{2} = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a^{2} is

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## The correct answer is: 2

### The given curve is , whose director circle is x^{2} + y^{2} = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)^{2} + 3a^{2} - 9 > 0 and (2a)^{2} + a^{2} - 12 < 0 i.e., .

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