Q40 / 60 · NEST (NISER) 2016 · Mathematics
For a positive real number $k$ let $E_k$ be the ellipse with equation
$\frac{x^2}{a^2+k}+\frac{y^2}{b^2+k}=1$
where $a \gt b \gt 0$. All members of the family of ellipses $\left\{E_k: k \gt 0\right\}$ have the same
$\frac{x^2}{a^2+k}+\frac{y^2}{b^2+k}=1$
where $a \gt b \gt 0$. All members of the family of ellipses $\left\{E_k: k \gt 0\right\}$ have the same
- Correct answerAfoci.
- Beccentricity.
- Cpair of directrices.
- Correct answerDcentre.
Hence, the correct answer is options: 'A', 'D'.