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Question

If the foci of an ellipse subtend a right angle at either extremity of its minor axis, then its eccentricity


A

Must be 12

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B

can be 12 or 32

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C

Must be 23

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D

Cannot be determined

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Solution

The correct option is A

Must be 12


Let ellipse be x2a2+y2b2=1

Its foci are S1(ae,0) and S2(ae,0) and the extremity of the minor axis is B(0,b)

Then

The product of slopes, mS1B×mS2B=1 [Because S1B and S2B are perpendicular]

(b00ae)(b00+ae)=1

b2=a2e2a2(1e2)=a2e2

1e2=e2e2=12e=12


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