Hyperbola 1 Question 13
14.
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 these
(1981, 2M)
Show Answer
Answer:
Correct Answer: 14. (b)
Solution:
- 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 $|r|<1$.
