A double ordinate of the parabola $y^{2} = 8 p x$ is of length $16 p$ . The angle subtended by it at the vertex of the parabola is

\frac{π}{4}

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\frac{π}{2}

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\frac{π}{3}

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none of these

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Solution

The correct option is A $\frac{π}{2}$
General formula,

for the parabola,

$y^{2} = 4 a x$

points are $P (α, 8 p)$

also, $P = (2 p t^{2}, 4 p t)$

$8 p = 4 p t$

$t = 2$

$∴ α = 8 p$

when, $tan \frac{θ}{2} = \frac{8 p}{8 p} = 1$

$∴ θ = \frac{π}{2}$

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