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In the standard ellipse, the lines joini...

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 (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`

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`

Text Solution

Verified by Experts

The correct Answer is:
D
`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`
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