Question
The circle on SS'as diameter touches the ellipse then the eccentricity of the ellipse is (where S and S'are the focus of the ellipse)
- 2/
- /2
- 1/
- None of these
/2
Hint:
assume the equation of an ellipse and find out the equation of the circle in terms of a,b and e.
The correct answer is: 1/
e> 1/√2
equation of ellipse : x2/a2+y2/b2=1
equation of circle : x2+y2=a2e2
on solving , we get
x2/a2+(a2e2 -x2 )/b2=1
here, D>0 since 2 real distinct roots exist.
This give us
e2> b2/a2
1-b2/a2>b2/a2
1>2b2/a2
b2/a2<1/2
- b2/a2>-1/2
1- b2/a2> 1-1/2
e2>1/2
e> 1/√2
for 2 distinct roots, discriminant value has to be greater than 0.
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