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

$x - a = y^{2}$

$x + a = y^{2}$

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

answer is B.

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Detailed Solution

Given $x = a + λ^{2}, y = b - λ$

$x - a = λ^{2} \dots \dots (1), y - b = - λ$

$λ = b - y$

$λ^{2} = {(b - y)}^{2} \dots \dots (2)$

From $(1) & (2)$ $(x - a) = {(b - y)}^{2}$

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