Consider the following coordinate transformation from familiar rectangular coordinates (x, y), labeling points in the plane...

    

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Consider the following coordinate transformation from familiar rectangular coordinates (x, y), labeling points in the plane to a new set of coordinates (. v): x=v. y = (-). (a) Sketch the curves of constant ju and constant v in the xy plane. (b) Transform the line element d'S2 dx2 + dy2 into (u, v) coordinates. (c) Do the curves of constant # and constant v intersect at right angles? (d) Find the equation of a circle of radius r centered at the origin in terms of u and v. (e) Calculate the ratio of the circumference to the diameter of a circle using (u, v) coordinates. Do you get the correct answer? Consider the following coordinate transformation from familiar rectangular coordinates (x, y), labeling points in the plane to a new set of coordinates (. v): x=v. y = (-). (a) Sketch the curves of constant ju and constant v in the xy plane. (b) Transform the line element d'S2 dx2 + dy2 into (u, v) coordinates. (c) Do the curves of constant # and constant v intersect at right angles? (d) Find the equation of a circle of radius r centered at the origin in terms of u and v. (e) Calculate the ratio of the circumference to the diameter of a circle using (u, v) coordinates. Do you get the correct answer?