UPSC NDA Math Model Paper 7

The given equation of the ellipse is 2x2+3y2=6
Divide throughout by 6 to get the equation in the standard form

x2

3

+

y2

2

=1
Therefore, a2=3 and b2=2
Now, for any ellipse using the relation we can write:
2=3(1−e2)
e2=

1

3

e=

1

√3

Therefore, the eccentricity of the given ellipse is

1

√3