Question

The question $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents

• A. an ellipse
• B. a hyperbola
• C. a circle
• D. None of these

Answer 1

The correct option is B a hyperbola

$\left|r\right|<1$

$\Rightarrow r^2<1\Rightarrow (r^2-1)<0$

$\Rightarrow r\in (-1,1)$

$\frac{x^2}{1-r}-\frac{y^2}{1+r}=1$

In given Domain of $r$, Equation represents a hyperbola.