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Find the equation of the ellipse whose f...

Find the equation of the ellipse whose focus is `S(-1, 1),` the corresponding directrix is `x -y+3=0,` and eccentricity is 1/2. Also find its center, the second focus, the equation of the second directrix, and the length of latus rectum.

Text Solution

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y-1=-1(x+1)
y=-x
CM=a/e=2a
CS=ae=a/2
SM=CM-CS=2a-a/2=3a/2
SM=`|(-1-1+3)/sqrt2|=3a/2`
after solving this
a=`sqrt2/3`
...
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