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Question

If the equation of the ellipse is 3x2+2y2+6x8y+5=0, then which of the following is/are true?

A
e=13
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B
Center is (1,2)
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C
Foci are (1,1) and (1,3)
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D
Directrices are y=2±3
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Solution

The correct options are
A e=13
B Center is (1,2)
D Foci are (1,1) and (1,3)
3x2+2y2+6x8y+5=0
(x+1)22+(y2)23=1
Therefore, centre is (1,2) and ellipse is vertical
(b>a)
a2=2,b2=3
Now 2=3(1e2)
e=13
Foci are (1,2±be) and (1,2±1).
Hence, the foci are (1,3) and (1,1)
The equations of the directrices are y=2±bey=5 and y=1

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