If `e_1a n d\ e_2` are respectively the eccentricities of the ellipse `(x^2)/(18)+(y^2)/4=1` and the hyperbola `(x^2)/9-(y^2)/4=1,` then the relation between `e_1a n d\ e_2` is a.`2e_1 ^2+e_2 ^2=3` b. `e_1 ^2+2e_2^ 2=3` c. `2e_1^ 2+e_2 ^2=3` d. `e_1 ^2+3e_2 ^2=2`

Explanation

As we given for ellipse

`a^2=18,b^2=4`

`impliese_1=sqrt(1−4/18)`

`=sqrt7/3`

And for hyperbola we have

`a^2=9,b^2=4`

`impliese_2=1+4/9=sqrt13/3`

Clearly, `2e_1^2+e_2^2=3`

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