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The focal distance of an end of the mino...

The focal distance of an end of the minor axis of the ellipse is k and the distance between the foci is 2h. Find the lengths of the semi-axes.

A

`(x^(2))/(h^(2)) +(y^(2))/(k^(2))=1`

B

`(x^(2))/(k^(2)) +(y^(2))/(k^(2)-h^(2))=1`

C

`x^(2)+(y^(2))/(k^(2)) =1`

D

`(x^(2))/(h^(2))+y^(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
B

Let the equation of the ellipse be `(x^(2))/(a^(2)) =(y^(2))/(b^(2))=1`
Given
`F_(1)F_(2)=2h " Also, "x+e x=k`
`rArr 2ae=2h rArr a+e(0)=k`
`rArr a e=h rArr a=k`
`:.b^(2)=a^(2)(1-e^(2)) =a^(2)-a^(2)e^(2) =k^(2)-h^(2)`
Equation of the ellipse is `(x^(2))/(k^(2)) +(y^(2))/(k^(2)-h^(2)) =1`
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