We call a coordinate system (u, v) orthogonal if its coordinate curves (the two families of curves u =constant and v =constant) are orthogonal trajectories (for example, a Cartesian coordinate system or a polar coordinate system). Let (u, v) be orthogonal coordinates, where u = x2+2y2, and x and y are Cartesian coordinates. Find the Cartesian equation of the v-coordinate curves, and sketch the (u, v) coordinate system.
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