Let H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1 be the hyperbola, whose eccentricity is \sqrt{3} and the length of the latus rectum is 4 \sqrt{3}. Suppose the point (\alpha, 6), \alpha > 0 lies on H. If \beta is the product of the focal distances of the point (\alpha, 6), then \alpha^2+\beta is equal to : [8 Apr 2024 Shift 1]

Hyperbola

Section: Mathematics

Question : 19 of 92

Marks: +1, -0

Let H:‌

−x2

+‌

=1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the point (α,6),α>0 lies on H. If β is the product of the focal distances of the point (α,6), then α2+β is equal to :

[8 Apr 2024 Shift 1]

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