Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix} a\\ b \end{pmatrix}= P \begin{pmatrix} x\\ y \end{pmatrix}$. Then $S$ is
1. A circle of radius $\sqrt{10}$.
2. A circle of radius $\frac{1}{\sqrt{10}}$
3. An ellipse with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
4. An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$