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If two tangents drawn from a point P to the parabola $y^{2} = 4 x$ be such that the slope of one tangent is double of the other, then P lies on the curve.

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$9 x^{2} = 2 y$

$9 y = 2 x^{2}$

$9 x = 2 y^{2}$

$2 x = 9 y^{2}$

answer is B.

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Detailed Solution

$a = 1, y = m x + 1 / m$ passing p(h, k) then

$k = m h + \frac{1}{m} \Rightarrow m^{2} h - m k + 1 = 0$

$m_{1} + m_{2} = \frac{k}{h}, m_{1} m_{2} = \frac{1}{h}$

$\Rightarrow 3 m_{2} = \frac{k}{h} & 2 m_{2} = \frac{1}{h} [∵ m_{1} = 2 m_{2}]$

$2 {(\frac{k}{3 h})}^{2} = \frac{1}{4} \Rightarrow 2 y^{2} = 9 x$

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