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Find the equation the conic whose focus ...

Find the equation the conic whose focus is `(1, -1)` eccentricity is `1/2` and the directrix is the line `x - y = 3.` Is the conic section an ellipse ?

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The correct Answer is:
`7x ^(2) + 2xy + 7y ^(2) - 10 x + 7 =0` yes it is an ellipse
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