Let one focus of the hyperbola H:(x²)/(a²)-(y²)/(b²)=1 be at (√(10),0) and the corresponding directrix be x=9/(√(10)). If e and l respectively are the eccentricity and the length of the latus rectum of H, then 9 (e²+l) is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q28

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

Let one focus of the hyperbola

H:\tfrac{x^2}{a^2}-\tfrac{y^2}{b^2}=1

be at

(\sqrt{10},0)

and the corresponding directrix be

x=\tfrac{9}{\sqrt{10}}

. If

e

and

l

respectively are the eccentricity and the length of the latus rectum of

H

, then

9\,(e^2+l)

is equal to: