Let \(P = \left[ {\begin{array}{*{20}{c}} 3&1\\ 1&3 \end{array}} \right]\) consider the set \(S\) of all vectors \(\left( {\begin{array}{*{20}{c}} x\\ y \end{array}} \right)\) such that \({a^2} + {b^2} = 1\) where \(\left( {\begin{array}{*{20}{c}} a\\ b \end{array}} \right) = P\left( {\begin{array}{*{20}{c}} x\\ y \end{array}} \right)\). This \(S\) is

• A. A circle of radius \(\surd 10\)
• 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 \(\left( {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right)\)