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JEE Main20244 Apr 2024Morning ShiftMathematicsHyperbolaActual

Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements is -3 . If the points (x, y) satisfying A ^2+x ~A +y I = O lie on a hyperbola, whose length of semi major axis is x and semi minor axis is y , eccentricity is e and the length of the latus rectum is l , then 81 (e^ 4+l^2 ) is equal to

Correct answer

0

Step-by-step solution

Given |A|=2 trace A=-3 and A ^2+ xA + yI =0 x =3, y =2 aligned & so, 81 e⁴=169 & L R=8 / 9 & 81 e⁴+81 L²=169+64=233 aligned

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