Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

Let A be a square matrix of order 2 such that |A|=2 and the sum of...

Let Abeasquarematrixoforder2suchthatA be a square matrix of order 2 such that|A|=2andthesumofitsdiagonalelementsis−3.Ifthepointsand the sum of its diagonal elements is -3 . If the points(x, y)satisfyingsatisfying\mathrm{A}^2+x \mathrm{~A}+y I\mathrm{I}=\mathrm{O}lieonahyperbola,whoselie on a hyperbola, whose\text { length of semi major axis is } x \text { and semi minor axis is } y,eccentricityis, eccentricity is\mathrm{e}andthelengthofthelatusrectumisand the length of the latus rectum isl,then, then81(e4+l2)\left(e^ 4+l^2\right) is equal to

Correct answer

233

Step-by-step solution

Given ∣A∣=2|A|=2 trace A=−3A=-3 and A2+xA+yI=0\mathrm{A}^2+\mathrm{xA}+\mathrm{yI}=0 ⇒x=3,y=2\Rightarrow \mathrm{x}=3, \mathrm{y}=2 so, 81e4=169LR=8/981e4+81L2=169+64=233\begin{aligned} & \text {so, } 81 e^{4}=169 \\ & L R=8 / 9 \\ & 81 e^{4}+81 L^{2}=169+64=233 \end{aligned}
Practice Hyperbola on Quantrex Academy →

More from Hyperbola

If the eccentricity e of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 , passing through… JEE Main 2026Let the eccentricity e of a hyperbola satisfy the equation 6e^2 - 11e + 3 = 0 . If the… JEE Main 2026Let H: (x^2)/(a^2)-(y^2)/(b^2)=1 be a hyperbola such that the distance between its foci… JEE Main 2026Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such… JEE Main 2026For some θ ∈(0, (π)/(2)) , let the eccentricity and the length of the latus rectum of the… JEE Main 2026Let PQ be a chord of the hyperbola x^ 2 4 - y^ 2 b^ 2 =1 , perpendicular to the x -axis… JEE Main 2026Let the domain of the function f(x)= _ 3 _ 5 _ 7 (9 x-x^ 2 -13) be the interval (m, n) .… JEE Main 2026Let P(10,2 15 ) be a point on the hyperbola x^ 2 a^ 2 - y^ 2 ~b^ 2 =1 , whose foci are S… JEE Main 2026If the line α x+2 y=1 , where α ∈ ℝ , does not meet the hyperbola x^ 2 -9 y^ 2 =9 , then… JEE Main 2026Let the foci of a hyperbola coincide with the foci of the ellipse x^ 2 36 + y^ 2 16 =1 .… JEE Main 2026Let e_1 and e_2 be the eccentricities of the ellipse x^2 ~b^2 + y^2 25 =1 and the… JEE Main 2025Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be… JEE Main 2025Consider the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having one of its focus at P(-3,0) . If… JEE Main 2025Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x^2 a^2 - y^2… JEE Main 2025If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x^2-y^2-α x+β y+γ=0… JEE Main 2025Let the product of the focal distances of the point P(4,2 3 ) on the hyperbola H: x^2 a^2… JEE Main 2025 Full Hyperbola list Hyperbola JEE Maths PYQsJEE Mathematics PYQs All Highly selective Backlog Qs for JEE Main PYQs