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?

Options

A. `(9)/(13)`
B. `(3)/(sqrt(13))`
C. `(2)/(sqrt(13))`
D. `(4)/(13)`

Answer

B

Explanation

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))`