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Prove that the eccentric angles of the extremities of latus recta of the ellipse x^2/a^2+y^2/b^2=1(a>b) is tan -1 (+-b/ae) please answer quickly

Prove that the eccentric angles of the extremities of latus recta of the ellipse x^2/a^2+y^2/b^2=1(a>b) is tan-1(+-b/ae)
please answer quickly
 
 

Grade:11

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
Let a cos @ = ae
b sin @ = ± b^2/a
 
b/a tan@ = ± b^2 /a^2 e
 
hence tan@ = ± b/ ae
 
hope it helps
 
Regards
Arun

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