Consider the curve defined by the equation $(2$x$^(2))/(9)+($xy$)/(9)+(5$y$^(2))/(36)=1.$

$($a$)(3$ points$)$ Let x$=$u$+2$v$,$y$=-2$u$+$v$.$ By plugging these into the original equation, find and fully

simplify an equation for the curve in terms of u and v$.$

$($b$)(1$ point$)$ What kind of conic is this, and what is its eccentricity?

Conic type:

Eccentricity: