VITEEE 2010 Paper

The equation of ellipse is
3x2+2y2+6x−8y+5=0
⇒ 3(x2+2x)+2(y2−4y)+5=0
⇒ 3(x2+2x+1)+2(y2−4y+4)+5−3−8=0
⇒3(x+1)2+2(y−2)2=6
⇒

(x+1)2

2

+

(y−2)2

3

=1
Comparing with

(x−h)2

a2

+

(y−k)2

b2

=1, we get
h=−1,k=2,a2=2,b2=3
Here, centre (h , k) = (-1, 2)
And using a2=b2(1−e2)
2=3(1−e2)⇒e=

1

√3

And foci are (h , k + be) and (h , k - be)
=(−1,2+1)‌and(−1,2−1)
=(−1,3)‌and(−1,1)