At any point on the parabola $y^{2} = 4 a x$
I: Length of the subtangent is twice the abscissa
II: Length of the subnormal is 4a.
Which of the above statements is correct?

Only I

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only II

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Both I and II

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neither I nor II

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Solution

The correct option is D Only I
$S T = (\frac{y}{M})$
$y^{'} = \frac{2 a}{y}$
$S T = | \frac{y^{2}}{2 a} |$
$S T = | \frac{4 a x}{2 a} |$
$= | 2 x |$
$S N = | y m |$
$= | y \times \frac{2 a}{y} |$
$= | 2 a |$
$\Rightarrow$ only 1 is true.

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