If the parabola $y^{2} = 4 a x$ passes through the point (3, 2), then the length of its latus rectum is

\frac{2}{3}

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\frac{4}{3}

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\frac{1}{3}

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Solution

The correct option is D $\frac{4}{3}$
in this equation of parabola is $y^{2} = 4 a x$ and the point is $(2, - 6)$
substitute $x = 3, y = 2$ in the equation of parabola

then we get,

$y^{2} = 4 a x$

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

$\Rightarrow 4 a = \frac{4}{3}$

hence the length of its latus rectum is $\frac{4}{3}$ .

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y^{2} = 4 a x

If the parabola $y^{2} = 4 a x$ passes through (-3,2), then length of its latus rectum is

y^{2} = 4 a x

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