Question

Let's consider the coordinates (u, v) such that x = u – v,y = u + v. (a) Find the inverse coordinate transformation-that is, (u, v) in terms of (x, y)-and sketch the lines of constant u and v. This should give you a strong hint about the rest of the answers. Write the line element dS? in terms of (u, v) and (du, dv). (c) The unit circle (i.e. circle of radius 1) is defined in Cartesian coordinates as x2+y2 = 1.Write that equation in terms of (u, v). Use that and your earlier sketch to describe in words how these coordinates differ from (x, y).

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