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If the curve x^(2)+3y^(2)=9 subtends an ...

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

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
The given curve is `(x^(2))/(9)+(y^(2))/(3) =1`, whose director circle is `x^(2) + y^(2) =12`.
For the required condition `(2alpha, alpha)` should lie inside the circle and outside the ellipse
i.e., `(2alpha)^(2) + 3alpha^(2) - 9 gt 0` and `(2alpha)^(2) + alpha^(2) - 12 lt 0`
i.e., `(9)/(7) lt alpha^(2) lt (12)/(5)`
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