Let \[{\text{P}} = \left[ {\begin{array}{*{20}{c}} 3&1 \\ 1&3 \end{array}} \right].\]   Consider the set S of all vectors \[\left( {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \end{array}} \right)\] such that a² + b² = 1 where \[\left( {\begin{array}{*{20}{c}} {\text{a}} \\ {\text{b}} \end{array}} \right) = {\text{P}}\left( {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \end{array}} \right).\]   Then S is

A. a circle of radius \[{\sqrt {10} }\]

B. a circle of radius \[\frac{1}{{\sqrt {10} }}\]

C. an ellipse with major axis along \[\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)\]

D. an ellipse with minor axis along \[\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)\]

Answer: Option D