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If the equation of the ellipse is 3x^2...

If the equation of the ellipse is `3x^2+2y^2+6x-8y+5=0` , then which of the following is/are true? (a) `e=1/(sqrt(3))` (b)Center is `(-1,2)dot` (c)Foci are `(-1,1)a n d(-1,3)dot` (d)Directrices are `y=2+-sqrt(3)`

A

` e = 1/sqrt(3)`

B

Center is (-1,2)

C

Foci are (-1,2)

D

Directrices are y=`2+-sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`3x^(2)+2y^(2)+6x-8y+5=0`
`or ((x+1)^(2))/(2)+((y-2)^(2))/(3)=1`
Therefore , the center is (1-2) and the ellipse is vertical (since `bgta)` ltrbgt `a^(2)=2, b^(2)=3`
Now, `2=3(1-e^(2))`
or `e=(1)/(sqrt(3))`
The foci `(-1,2+-be ) and (-1,2+-1)`, i.e., (-1,3) and )-1,1) Teh directrices are `y=2+-b//oe or y=5 and y=-1`
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