In the coordinate plane, for point $\mathrm { A } ( 0,4 )$ and point P on the ellipse $\frac { x ^ { 2 } } { 5 } + y ^ { 2 } = 1$, let Q be the point other than A among the two points where the line passing through A and P meets the circle $x ^ { 2 } + ( y - 3 ) ^ { 2 } = 1$. When point P passes through all points on the ellipse, what is the length of the figure traced by point Q? [3 points] (1) $\frac { \pi } { 6 }$ (2) $\frac { \pi } { 4 }$ (3) $\frac { \pi } { 3 }$ (4) $\frac { 2 } { 3 } \pi$ (5) $\frac { 3 } { 4 } \pi$
In the coordinate plane, for point $\mathrm { A } ( 0,4 )$ and point P on the ellipse $\frac { x ^ { 2 } } { 5 } + y ^ { 2 } = 1$, let Q be the point other than A among the two points where the line passing through A and P meets the circle $x ^ { 2 } + ( y - 3 ) ^ { 2 } = 1$. When point P passes through all points on the ellipse, what is the length of the figure traced by point Q? [3 points]\\
(1) $\frac { \pi } { 6 }$\\
(2) $\frac { \pi } { 4 }$\\
(3) $\frac { \pi } { 3 }$\\
(4) $\frac { 2 } { 3 } \pi$\\
(5) $\frac { 3 } { 4 } \pi$