In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is `sqrt(10) - sqrt(5)`. The equation of the ellipse

Options

A. `(x^(2))/(36) +(y^(2))/(18) = 1`
B. `(x^(2))/(40)+(y^(2))/(20) = 1`
C. `(x^(2))/(20) +(y^(2))/(10) = 1`
D. `(x^(2))/(10)+(y^(2))/(5) =1`

Answer

D

Explanation

`ae = b rArr e^(2) = (b^(2))/(a^(2)) rArr e^(2) =1 -e^(2)`
`:. e = (1)/(sqrt(2))`
Also `SA = a- ae = sqrt(10) - sqrt(5)`
`:. a (1-(1)/(sqrt(2))) = sqrt(10) (1-(1)/(sqrt(2))):. a^(2) = 10 rArr b^(2) = 5`