Let $R^2$ have the inner product $($:$u,v$:$)=5u_1{v}_1+5u_2{v}_2,$ and let $x=(1,2)$ and $y=(5,-1).$

a$.$ Find $||x||,||y||,$ and $|($:$x,y$:$){|}^2.$

b$.$ Describe all vectors $(z_1,z_2)$ that are orthogonal to $y.$

a$.$ Find $||x||,||y||,$ and $|($:$x,y$:$){|}^2.$

$||x||=,($Simplify your answer. Type an exact answer, using radicals as needed.$)$