Let the sum of the focal distances of the point P(4,3) on the hyperbola H: (x²)/(a²)-(y²)/(b²)=1 be (8√(5))/3. If for H, the length of the latus rectum is l and the product of the focal distances of the point P is m, then 9l²+6m is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q110

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

Let the sum of the focal distances of the point P(4,3) on the hyperbola

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

\tfrac{8\sqrt{5}}{3}

. If for

H

, the length of the latus rectum is

l

and the product of the focal distances of the point

P

m

, then

9l^2+6m

is equal to:

JEE Main 2025 Coordinate Geometry Question with Solution (April Unspecified (session-level dataset), Q110) | JEE Arc