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The foci of an ellipse are (-2,4) and (2...

The foci of an ellipse are `(-2,4)` and (2,1). The point `(1,(23)/(6))` is an extremity of the minor axis. What is the value of the eccentricity?

A

`(9)/(13)`

B

`(3)/(sqrt(13))`

C

`(2)/(sqrt(13))`

D

`(4)/(13)`

Text Solution

Verified by Experts

The correct Answer is:
B
Foci are `A(-2,4)` and `B(2,1)`
`:. AB = 2ae = 5`
Center is midpoint of AB which is `C(0,5//2)` Distance of center from extremity of minor axis which is `D(1,23//6)` is 'b'
`:. b = (5)/(3)`
Now, `b^(2) = a^(2) - a^(2)e^(2)`
`rArr a^(2) = b^(2) + a^(2)e^(2) = (325)/(36)`
`rArr e^(2) = 1 - (b^(2))/(a^(2)) = (3)/(sqrt(13))`
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