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# Please help! A double ordinate of the parabola y2= 8 px is of length 16p. The angle subtended by it at the vertex of the parabola is

A double ordinate of the parabola y2 = 8 px is of length 16p. The angle subtended by it at the vertex of the parabola is

• Option 1)

$\frac{\pi}{4}$

• Option 2)

$\frac{\pi}{2}$

• Option 3)

$\frac{\pi}{3}$

• Option 4)

none of these

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Length of the latus rectum -

$4a$

- wherein

For the parabola.

$y^{2}=4ax$

&

End point of latus rectum -

$\left ( a,2a \right )\: and\: \left ( a,-2a \right )$

- wherein

For the parabola.

$y^{2}=4ax$

$P\equiv (\alpha, 8P)$

Also, $P= (2pt^{2}, 4pt)$

Now, $8p= 4pt \Rightarrow t=2$

So, $\alpha = 8p$

angle subtended $= \theta$    when, $\tan \frac{\theta }{2} = \frac{8p}{8p} = 1$

So, $\theta =90^{\circ} = \frac{\pi }{2}$

Option 1)

$\frac{\pi}{4}$

This solution is incorrect

Option 2)

$\frac{\pi}{2}$

This solution is correct

Option 3)

$\frac{\pi}{3}$

This solution is incorrect

Option 4)

none of these

This solution is incorrect

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