For two points $\mathrm { A } ( 1 , \sqrt { 3 } ) , \mathrm { B } ( 1 , - \sqrt { 3 } )$ on the coordinate plane, what is the total length of the figure represented by point $\mathrm { P } ( x , y )$ satisfying the following two conditions? [4 points] (가) $x ^ { 2 } + y ^ { 2 } = 4$ (나) For any point $( 1 , a )$ on segment AB, the matrix $\left( \begin{array} { c c } x & y \\ 1 & a \end{array} \right)$ has an inverse matrix. (1) $\frac { 1 } { 3 } \pi$ (2) $\frac { 1 } { 2 } \pi$ (3) $\pi$ (4) $\frac { 4 } { 3 } \pi$ (5) $\frac { 3 } { 2 } \pi$
For two points $\mathrm { A } ( 1 , \sqrt { 3 } ) , \mathrm { B } ( 1 , - \sqrt { 3 } )$ on the coordinate plane, what is the total length of the figure represented by point $\mathrm { P } ( x , y )$ satisfying the following two conditions? [4 points]\\
(가) $x ^ { 2 } + y ^ { 2 } = 4$\\
(나) For any point $( 1 , a )$ on segment AB, the matrix $\left( \begin{array} { c c } x & y \\ 1 & a \end{array} \right)$ has an inverse matrix.\\
(1) $\frac { 1 } { 3 } \pi$\\
(2) $\frac { 1 } { 2 } \pi$\\
(3) $\pi$\\
(4) $\frac { 4 } { 3 } \pi$\\
(5) $\frac { 3 } { 2 } \pi$