Question
Mathematics Question on Ellipse
Let S and S′ be the foci of an ellipse and B be one end of its minor axis. If SBS′ is an isosceles right angled triangle then the eccentricity of the ellipse is
A
21
B
21
C
23
D
31
Answer
21
Explanation
Solution
We have,
SBS′ is an isosceles right angle triangle.
∴SS2=SB2+S′B2
⇒(2ae)2=b2+(ae2+b2+(ae)2
⇒4(ae)2=2(b2+(ae)2)
⇒(ae)2=b2
⇒e2=a2b2
⇒1−e2=1−a2b2
⇒1−e2=e2[∵e=1−a2b2]
⇒2e2=1
⇒e=21