If the extremities of the latus rectum of the ellipse x225+y216=1 is (α,β), then the distance between the point P(1,1) and (α,β), when α>0 is/are
A
√22125units
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B
√2215units
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C
√5415units
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D
√54125units
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Solution
The correct option is C√5415units Given equation of ellipse is x225+y216=1
It is in the form of x2a2+y2b2=1
Where a=5 and b=4
Clearly a>b
Now, e2=1−b2a2⇒e2=1−1625⇒e=35
The coordinates of the extremities of the latus rectum are (±ae,±b2a) ⇒(α,β)=(±3,±165)
Since α>0, then coordinates are (3,165) and (3,−165)
∴ Distance between (1,1) and (3,165) =√(1−3)2+(1−165)2=√2215units
And the distance between (1,1) and (3,−165) =√(1−3)2+(1+165)2=√5415units