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Question

An ellipse passing through the point (213,4) has its foci at (4,1) and (4,1), then its eccentricity is

A
23
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B
13
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C
14
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D
12
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Solution

The correct option is C 12
Let foci A=(4,1)B=(4,1) and point be P=(213,4)
Distance between foci is AB=2ae=(4+4)2=8
AP+BP=2a
AP=(4+213)2+(41)2=16+1613+52+9
=77+1613=64+13+2×8×13
=(8+13)2=8+13
Similarly BP=(4213)2+(41)2=771613=813
AP+BP=8+13+813=16
Therefore e=ABAP+BP=816=12

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