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hey how to find eccentric angles at the end points of latus rectum of the ellipse x sq by 4 PLUS y sq = 1 ?

hey how to find eccentric angles at the end points of latus rectum of the ellipse x sq by 4 PLUS y sq = 1 ?


 

Grade:12th Pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans: 30
Sol:
Ellipse:
\frac{x^{2}}{4}+y^{2}=1
Let the end of the latus rectum on the ellipse be P & Q. Then
P(acos\theta , bsin\theta )
Q(acos\theta , -bsin\theta )
Since latus rectum passes through focus, we have
acos\theta =ae
cos\theta =e
e^{2} = 1 - \frac{b^{2}}{a^{2}} = 1- \frac{1}{4} = \frac{3}{4}
e= \frac{\sqrt{3}}{2}
cos\theta = \frac{\sqrt{3}}{2}
\theta = cos^{-1}\frac{\sqrt{3}}{2}
\theta = 30
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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