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If (5,12) and (24,7) are the foci of an ellipse passing through the origin and if e is the eccentricity, then the value of \mathrm{\left[\frac{1}{e}\right]}, where \mathrm{[\cdot]} represents the greatest integer function, is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

If the two foci are \mathrm{S(5,12)}$  and S^{\prime}(24,7) and it passes through the origin O, then

\mathrm{ S O=\sqrt{25+144}=13 \text { and } S^{\prime} O=\sqrt{576+49}=25 }
and 

\mathrm{S S^{\prime}=\sqrt{386}}

If the conic is an ellipse, then \mathrm{S O+S^{\prime} O=2 a \, \, and \, \, S S^{\prime}=2 a e.}

Therefore, \mathrm{e=\frac{S S^{\prime}}{S^{\prime} O+S O}=\frac{\sqrt{386}}{38}}

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sudhir.kumar

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