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The ball of capacity a, denoted B(a), is the ball with \\pi r^2 \\le a.\n  We show P(1,2) embeds in B^4(a) if and only if a is at least 3. This shows the inclusion of P(1,2) in B^4(3) is optimal. The necessity of a \\ge 3 implies that for this particular embedding problem neither the Ekeland-Hofer nor ECH capacities give a sharp obstruction. 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