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

 

Answers (1)
V Vakul

 

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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