Let H: (-x²)/(a²)+(y²)/(b²)=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

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 8 Apr, Morning shift · Q3982

JEE Main 20248 Apr, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

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