If for the matrix, $$A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$$, $$A{A^T} = {I_2}$$, then the value of $${\alpha ^4} + {\beta ^4}$$ is :

If the curve x² + 2y² = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x $$-$$ y + 4z = 8

A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :