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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

- A circle of radius $\sqrt{10}$.
- A circle of radius $\frac{1}{\sqrt{10}}$
- An ellipse with major axis along $\begin{pmatrix}

1\\

1

\end{pmatrix}$ - An ellipse with minor axis along $\begin{pmatrix}

1\\

1

\end{pmatrix}$

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