Question

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

Answer 1

`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`