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  • The angle made by a double ordinate of length 12 a at the vertex of the parabola <img alt="\mathrm{y^2=4 a x}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%5E2%3D4%20a%20x%7D"

The angle made by a double ordinate of length 12 a at the vertex of the parabola \mathrm{y^2=4 a x} is
 

Option: 1

\mathrm{ \frac{\pi}{ 2 }}


Option: 2

\mathrm{ \tan ^{-1}\left(\frac{12}{5}\right) }


Option: 3

\mathrm{ \tan ^{-1}(2)}


Option: 4

 none of these
 


Answers (1)

best_answer

Let P Q be a double ordinate of length 12 a. Then coordinate of P will be \mathrm{(9 a, 6 a)} and of Q will be \mathrm{(9 a, -6 a)}. Slope of O P will be \mathrm{\frac{2}{3}} so the chord P Q will subtend the angle \mathrm{\tan ^{-1}\left(\frac{2(\frac{2}{3})}{1-(\frac{4}{9})}\right)=\tan ^{-1} \frac{12}{5}}

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