Question

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

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

Answer 1

Answer: (B)

a hyperbola

Answer 2

Given equation is $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,Where |r|<1$
$\Rightarrow$ $1-r is (+ve) and 1+r is (+ve)$
$\therefore$ Given equation is of the form$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$
Hence, it represents a hyperbola when $|r|<1.$