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2 AnswersLast Activity: 14 Years ago
Dear student,
The eccentricity of an ellipse is defined as the ratio of the distance between any point in the ellipse and the focus and distance between point and a fixed line called directrix.
e = distance between P and F/distance between P and line D (Directrix)
Formula for eccentricity :
Formula for calculating e is
b2 = (a2)(e2-1) So e2- 1 = b2/a2 or e2 = b2/a2 +1
e = √(b2/a2+1)
Eccenticity = square root of square of semi minor axis divided by squares of semi major axis
Last Activity: 14 Years ago
eccentricity of hyperbola = 1+b2/a2 = e ..............1
eccentricity of conjugate = 1+a2/b2 = ec2 ..................2 (ec = eccentricity of conjugate hyperbola)
from these two equatns , ec = e/(e2-1)1/2 ......................3
f(f(e)) = e (n = 2 even)
f(f(f(e))) = e/(e2-1)1/2 (n = 3 odd)
now , if n = even then
integral ede = e2/2 lim from 1 to 3
=4 (A)
if n = odd then
integral ede/(e2-1)1/2 lim 1 to 3
= (e2-1)1/2 lim 1 to 3
=2root2 (D)
hence option A,D are correct ....
approve if u like my ans
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