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$S_{1} :$ The equation $y^{2} = 4 a x$ represents parabola with the focus at (2a,0)
$S_{2} :$ The parabolas $y^{2} = 4 a x$ and $x^{2} = 4 b y$ are always orthogonal to each other. Then

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$S_{1}$ is false and $S_{2}$ is true

$S_{2}$ is false

$S_{1}$ is true

Both $S_{1}$ & $S_{2}$ are true

answer is B.

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Detailed Solution

$S_{1} :$ The focus of the parabola $Y^{2} = 4 a x is (a, 0)$

$S_{2} :$ The tangents at the intersection of the parabolas are perpendicular to each other

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