13. In the Cartesian coordinate plane, the hyperbola $\Gamma$ is centered at the origin with one focus at $( \sqrt { 5 } , 0 )$ . $\overrightarrow { e _ { 1 } } = ( 2,1 )$ and $\overrightarrow { e _ { 2 } } = ( 2 , - 1 )$ are direction vectors of the two asymptotes respectively. For any point $P$ on the hyperbola $\Gamma$ , if $\overrightarrow { O P } = a \overrightarrow { e _ { 1 } } + b \overrightarrow { e _ { 2 } } ( a , b \in \mathbf { R } )$ , then an equation satisfied by $a$ and $b$ is $\_\_\_\_$.
(5 points) The equation of the circle with center at the origin that is tangent to the line $x + y - 2 = 0$ is $\_\_\_\_$.
13. In the Cartesian coordinate plane, the hyperbola $\Gamma$ is centered at the origin with one focus at $( \sqrt { 5 } , 0 )$ . $\overrightarrow { e _ { 1 } } = ( 2,1 )$ and $\overrightarrow { e _ { 2 } } = ( 2 , - 1 )$ are direction vectors of the two asymptotes respectively. For any point $P$ on the hyperbola $\Gamma$ , if $\overrightarrow { O P } = a \overrightarrow { e _ { 1 } } + b \overrightarrow { e _ { 2 } } ( a , b \in \mathbf { R } )$ , then an equation satisfied by $a$ and $b$ is $\_\_\_\_$.