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The foci of an ellipse are S(-1,-1), S'(...

The foci of an ellipse are `S(-1,-1), S'(0,-2) `its `e=1/2`, then the equation of the directrix corresponding to the focus S is

A

x-y+3-=0

B

x-y+7=0

C

x-y+5=0

D

x-y+4=0

Text Solution

Verified by Experts

Foci are S(-1,-1) and S'(0,-2)
Thus, center is` C(-1/2,-3/2)`
`2ae=SS'=sqrt(2)`
`:. q=sqrt(2)`
Now, directrix is at distance `(a)/(e)` from the centre.
So, we have to find equation of line at distance `2sqrt(2)` from C(-1/2,-3/2).
Also, slop of axis is equal to -1
Thus, equation of directrix is y=x+c.
Its distance from center is `2sqrt(2)`
`:.(|-(1)/(2)+(3)/(2)+c|)/(sqrt(2))=2sqrt(2)`
`:. c=5 or 3`
Therefore, directrix is x-y+3=0` (as it is nearer to focus S) .
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