Question: 1. Given a E R, let Ca = {(x, y) ER' | y' - ar' +x = 0}. (a) Sketch Ca for a = -1,

1. Given a E R, let Ca = {(x, y) ER' | y' - ar' +x = 0}. (a) Sketch Ca for a = -1, a = 0, and a = 1. Then, explain how Ca changes as a varies. (You may use graphing software to help you if you wish.) (b) Show that ya : R -> R2 given by Ya(t) = (a-12, at-+ ) is a (smooth) parametrization of Ca. Is it a parametrization of the entire curve, or are any points missed? Justify your answer. (c) For which a is Ya regular

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