Question

A circle is described with minor axis of the ellipse as diameter if the foci lie on the circle then the eccentricity of the ellipse is

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The length of the minor axis=2b

The distance between the foci=2ae

The line segment joining the foci is bisected perpendicular by the minor axis.

Hence the line segment joining the foci should also be a diameter. Hence they are equal.

2b=2ae

b=ae

b

2

=a

2

e

2

a

2

(1−e

2

)=a

2

e

2

1−e

2

=e

2

1=2e

2

e

2

=

2

1

e=

2

1

Hence the eccentricity =

2

1

.