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Q.

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

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a

x :y

b

2 : 1

c

1:1

d

$x^{2} : y$

answer is B.

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Detailed Solution

$\frac{S.T.}{x} = \frac{y}{y^{'} \cdot x}$ $\to (1)$

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$from y^{2} = 4 a x ⇒ 2 y y^{'} = 4 a \Rightarrow y^{'} = \frac{2 a}{y}$

Putting $y^{1}$ in (1) the ratio is $\frac{y^{2}}{2 a x} = \frac{4 a x}{2 a x} = \frac{2}{1}$

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