For the parabola $y^{2} = 4 a x$ , the ratio of the subtangent to the abscissa is?

1 : 1

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2 : 1

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x x : y

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x^{2} : y^{2}

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Solution

The correct option is B $2 : 1$
Sub-tangent = $\frac{y}{\frac{d y}{d x}}$
$2 y \frac{d y}{d x} = 4 a$
$\frac{d y}{d x} = \frac{2 a}{y}$
Sub-tangent = $\frac{y}{\frac{d y}{d x}}$
$⟹ \frac{y^{2}}{2 a}$
$⟹ \frac{4 a x}{2 a} = 2 x$
Ratio of the subtangent to the abscissa = $\frac{2 x}{x} = 2 : 1$

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