Find the eccentricity of the ellipse 2x²+3y²=6

Correct Answer is : 13{1}{{3}}31

Correct Answer is : 13{1}{{3}}31

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UPSC NDA Math Model Paper 7

Question : 11 of 120

Marks: +1, -0

2x^{2}+3y^{2}=6

Solution:

The given equation of the ellipse is

2x^{2}+3y^{2}=6

Divide throughout by 6 to get the equation in the standard form

\frac{x^{2}}{3}+\frac{y^{2}}{2}=1

Therefore,

a^{2}=3

and

b^{2}=2

Now, for any ellipse using the relation we can write:

2=3(1-e^{2})

e^{2}=\frac{1}{3}

e=\frac{1}{\sqrt{3}}

Therefore, the eccentricity of the given ellipse is

\frac{1}{\sqrt{3}}

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