Let a line $L$ pass through the point of intersection of the lines $b x + 10 y - 8 = 0$ and $2 x - 3 y = 0$, $b \in R - \left\{ \frac { 4 } { 3 } \right\}$. If the line $L$ also passes through the point $( 1,1 )$ and touches the circle $17 \left( x ^ { 2 } + y ^ { 2 } \right) = 16$, then the eccentricity of the ellipse $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is (1) $\frac { 2 } { \sqrt { 5 } }$ (2) $\sqrt { \frac { 3 } { 5 } }$ (3) $\frac { 1 } { \sqrt { 5 } }$ (4) $\sqrt { \frac { 2 } { 5 } }$
Let a line $L$ pass through the point of intersection of the lines $b x + 10 y - 8 = 0$ and $2 x - 3 y = 0$, $b \in R - \left\{ \frac { 4 } { 3 } \right\}$. If the line $L$ also passes through the point $( 1,1 )$ and touches the circle $17 \left( x ^ { 2 } + y ^ { 2 } \right) = 16$, then the eccentricity of the ellipse $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ is\\
(1) $\frac { 2 } { \sqrt { 5 } }$\\
(2) $\sqrt { \frac { 3 } { 5 } }$\\
(3) $\frac { 1 } { \sqrt { 5 } }$\\
(4) $\sqrt { \frac { 2 } { 5 } }$