Let $S=\left\{(x, y) \in R^2: \frac{y^2}{1+r}-\frac{x^2}{1-r}=1\right\}$, where where $r \neq \pm 1$. Then $S$ represents
Select the correct option:
A
An ellipse whose eccentricity is $\frac{1}{\sqrt{\mathrm{r}+1}}$, when $\mathrm{r}>1$.
B
An ellipse whose eccentricity is $\sqrt{\frac{2}{\mathrm{r}+1}}$, when $\mathrm{r}>1$.
C
A hyperbola whose eccentricity is $\frac{2}{\sqrt{\mathrm{r}+1}}$, when $0<\mathrm{r}<1$. (4) A hyperbola whose eccentricity is $\frac{2}{\sqrt{1-\mathrm{r}}}$, when $0<\mathrm{r}<1$.
D
A hyperbola whose eccentricity is $\frac{2}{\sqrt{1-\mathrm{r}}}$, when $0<\mathrm{r}<1$.
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