If `e_1` is the eccentricity of the conic `9x^2+4y^2=36\ a n d\ e_2` is the eccentricity of the conic `9x^2-4y^2=36` then a. `e_1 ^2-e_2^ 2=2` b. `e_2 ^2-e_1 ^2=2` c. 2< `e_2^2-e_1^2<3` d.`e_1^2-e_2^2>3`

Explanation

`frac{9 x^{2}}{36}+frac{4 y^{2}}{36}=1 `

`Rightarrow frac{x^{2}}{4}+frac{y^{2}}{9}=1`

`therefore b^{2}=a^{2}(1-e_{1})^{2} `

`Rightarrow 9=4(1-e_{1})^{2} `

`Rightarrow(e_{1})^{2}=frac{-5}{4}`

The conic

`9 x^{2}-4 y^{2}=36` can rewritten as

`frac{9 x^{2}}{36}-frac{4 y^{2}}{36}=1 `

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