Find the length of subnormal to $y^{2} = 4 a x$ at $(a t^{2}, 2 a t)$

2 a

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a

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a / 2

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4 a

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Solution

The correct option is C $2 a$
$y^{2} = 4 a x$
$∴ \frac{d y}{d x} = \frac{2 a}{y}$
Therefore, Length of subnormal $= ∣ ∣ ∣ y \frac{d y}{d x} ∣ ∣ ∣ = ∣ ∣ ∣ (y) (\frac{2 a}{y}) ∣ ∣ ∣ = 2 a$
So, the answer is option (A).

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