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An ellipse, with foci at (0, 2) and (0, ...

An ellipse, with foci at (0, 2) and (0, –2) and minor axis of length 4, passes through which of the following points?

A

`(sqrt(2),2)`

B

`(2,sqrt(2))`

C

`(2,2sqrt(2))`

D

`(1,2sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the equation of ellipse be
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
since . Foci are at (0, 2) and (-2,0) , major axis is along the Y- axis .
SO , be = 2
[ where e is the eccentricity of ellipse ]
and 2a= length of minor axis =4 [ given]
`implies alpha =2`.. . . (iii)
`:' e^(2) =1-(a^(2))/(b^(2))`
`therefore ((2)/(b) )^(2)=1-(4)/(b^(2))`
` implies (8) /(b^(2)) =1implies b^(2) =8`
thus equation of required ellipse is `(^(2))/(4)+(y^(2))/(8)=1`
now , from the option the ellipse `(x^(2))/(4)+(y^(2))/(8)=1` passes through the point `(sqrt(2),2)`.
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