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An ellipse has the points (1, -1) and (2...

An ellipse has the points `(1, -1) and (2,-1)` as its foci and `x + y = 5` as one of its tangent then the value of `a^2+b^2` where `a,b` are the lenghta of semi major and minor axes of ellipse respectively is :

A

`(41)/(2)`

B

10

C

19

D

`(81)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`2ae = SS' =1`
`p_(1)p_(2) = b^(2)`, where `p_(1)` and `p_(2)` are the length of perpendicular from S and S' to the tangent
`(5)/(sqrt(2)). (4)/(sqrt(2)) = b^(2)`
`rArr b^(2) = 10`
`rArr b^(2) = 10 = a^(2) - e^(2)a^(2)`
`rArr a^(2) = (41)/(4)`
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