A) a hyperbola whose eccentricity is\[\frac{2}{\sqrt{1-r}},\]when
B) an ellipse whose eccentricity is\[\sqrt{\frac{2}{r+1}},\]when
C) a hyperbola whose eccentricity is \[\frac{2}{\sqrt{r+1}},\] when
D) an ellipse whose eccentricity is \[\frac{1}{\sqrt{r+1}},\] when
Correct Answer: B
Solution :
\[\frac{{{y}^{2}}}{1+r}-\frac{{{x}^{2}}}{1-r}=1\] |
\[r>1\]\[\Rightarrow \]ellipse |
\[e=\sqrt{1-\left( \frac{r-1}{r+1} \right)}=\sqrt{\frac{2}{r+1}}\] |
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