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The distance between directrix of the el...

The distance between directrix of the ellipse `(4x-8)^(2)+16y^(2)=(x+sqrt(3)y+10)^(2)` is

A

12

B

16

C

20

D

24

Text Solution

Verified by Experts

The correct Answer is:
B
`(4x -8)^(2) + 16y^(2) = (x+sqrt(3)y + 10)^(2)`
`rArr (x-2)^(2)+y^(2) =((1)/(2))^(2) ((x+sqrt(3)y+10)^(2))/(4)`
Focus is `(h,k) = (2,0), e= (1)/(2)` and directrix `x + sqrt(3)y + 10 =0 (a)/(e) - ae =` perpendicular distance from (2,0) to directrix
`x + sqrt(3)y + 10 =0`
`rArr 2a - (a)/(2) = (|2+0+10|)/(2)`
`rArr (3a)/(2) = 6 rArr a = 4`
`:.` Distance between directrix `=(2a)/(e) = (2.4)/(1//2) = 16`
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