Statement-I : Two perpendicular normals can be drawn from the point $(\frac{5}{2}, - 2)$ to the parabola ${(y + 2)}^{2} = 2 (x - 1) .$
Statement-II : Two perpendicular normals can be drawn from the point $(3 a, 0)$ to the parabola $y^{2} = 4 a x .$

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Statement-I is false but statement-II is true

Both statement-I and statement-II are false but statement-II is correct explanation of statement-I

Both statement-I and statement-II are true but statement-II is not correct explanation of statement-I

Statement-I is true statement-II is false

answer is B.

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Detailed Solution

The vertex of ${(y + 2)}^{2} = 2 (x - 1)$ is $(1, - 2)$ and equation of axis is $y = - 2.$
Here, $4 a = 2$
$∴ a = \frac{1}{2} \Rightarrow 3 a = \frac{3}{2}$
$∴$ Required point is $(1 + \frac{3}{2}, - 2), i . e ., (\frac{5}{2}, - 2) .$
Hence, both statements are true and statement-II is correct explanation for Statement-I.