Question
An ellipse has OB as semi minor axis, F and F ^ its focii and the angle FBF' is a right angle. Then the eccentricity of the ellipse is
BITSAT
Mathematics
Ellipse
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. 1 2
- B. 1 2
- C. 1 4
- D. 1 3
Answer
A. 1 2
Step-by-step solution
FBF ^ =90^ FB ^ 2 + F ^ B ^ 2 = FF ^ 2 ( a^ 2 e^ 2 +b^ 2 )^ 2 + ( a^ 2 e^ 2 +b^ 2 )^ 2 =(2 a e)^ 2 2 (a^ 2 e^ 2 +b^ 2 )=4 a^ 2 e^ 2 e^ 2 = b^ 2 a^ 2 Also e^ 2 =1- b^ 2 a^ 2 =1-e^ 2 array l 2 e^ 2 =1 \\ e= 1 2 array
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