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  • The length of latus rectum of he parabola, whose focus is <img alt="\mathrm{(a \sin 2 \theta, a \cos 2 \theta)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28a%20%5Csin%202%2

The length of latus rectum of he parabola, whose focus is \mathrm{(a \sin 2 \theta, a \cos 2 \theta)} and directrix is the line \mathrm{\mathrm{y}=\mathrm{a}}, is
 

Option: 1

\mathrm{\left|\mathrm{ra} \cos ^2 \theta\right|}


 


Option: 2

\mathrm{\left|4 \mathrm{a} \sin ^2 \theta\right|}
 


Option: 3

\mathrm{|4 a \cos 2 \theta|}
 


Option: 4

\mathrm{|a \cos 2 \theta|}


Answers (1)

best_answer

Distance of focus from directrix is \mathrm{|a \cos 2 \theta-a|}. Thus length of latus rectum is \mathrm{\left|4 a \sin ^2 \theta\right|}.

Hence option 2 is correct.

Posted by

chirag

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