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 $\begin{pmatrix}
1\\
1
\end{pmatrix}$