Question
Question: If α and β are the eccentric angles of the extremities of a focal chord of an standard ellipse, then...
If α and β are the eccentric angles of the extremities of a focal chord of an standard ellipse, then the eccentricity of the ellipse is
A
cos(α+β)cosα+cosβ
B
sin(α−β)sinα−sinβ
C
cos(α−β)cosα−cosβ
D
sin(α+β)sinα+sinβ
Answer
sin(α+β)sinα+sinβ
Explanation
Solution
axcos2α+β+bysin2α+β=cos2α−β; aaecos2α+β=cos2α−β⇒e=cos2α+βcos2α−β.2sin2α+β2sin2α+β=sin(α+β)sinα+sinβ.