Let H:(x²)/(a²) - (y²)/(b²) = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(2 2 + √(14)). If the eccentricity H is (√(11))/2, then the value of a² + b² is equal to _ _ _ _ _.

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jun, Morning shift · Q39

JEE Main 202229 Jun, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let

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

, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is

4(2\sqrt 2 + \sqrt {14} )

. If the eccentricity H is

{{\sqrt {11} } \over 2}

, then the value of a² + b² is equal to __________.

Your answerType your answer. Integers and decimals are accepted.