Question

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 \(A^{2}+x A+y I=0\) lie on a hyperbola, whose transverse axis is parallel to the x-axis, eccentricity is e and the length of the latus rectum is l, then \(\mathrm{e}^{4}+ l^{4}\) is equal to _____.

Answer 1

Correct answer: 25

Given \(|\mathrm{A}|=2\)

trace \(\mathrm{A}=-3\)

and \(\mathrm{A}^{2}+\mathrm{xA}+\mathrm{yI}=0\) 

\(\Rightarrow \mathrm{x}=3, \mathrm{y}=2\)

So, information is incomplete to determine eccentricity of hyperbola (e) and length of latus rectum of hyperbola (l).