If the curve x² + 3y² = 9 subtends an obtuse angle at the point (2a, a), then a possible value of a² is

The correct answer is: 2

The given curve is , whose director circle is x² + y² = 12. For the required condition (2a, a) should lie inside the circle and outside the ellipse i.e.,(2a)² + 3a² - 9 > 0 and (2a)² + a² - 12 < 0 i.e., .