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The locus of the point $x = a + λ^{2}$ $, y = b - λ$ where $λ$ is a parameter is

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$x - a = {(b - y)}^{2}$

$x + a = y^{2}$

${(x - a)}^{2} = b - y$

$x - a = y^{2}$

answer is B.

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Detailed Solution

$Given x = a + λ^{2}, y = b - λ \Rightarrow x - a = λ^{2} \to ①, b - y = λ - ② from ① & ② (x - a) = {(b - y)}^{2}$

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