For the parabola $y^{2} = 16 x$ , the ratio of the length of the sub-tangent to the abscissa at any point on the curve is

1 : 1

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2 : 1

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x : y

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x^{2} : y

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Solution

The correct option is C $2 : 1$
$2 y^{'} y = 16$
$y^{'} = \frac{8}{y}$
$S T = (\frac{y}{m})$
$= | \frac{y^{2}}{8} |$
$= \frac{16 x}{8}$
$= 2 x$
$\frac{S T}{x} = \frac{2}{1}$

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