Let s= (x, y) R^ 2 : y^ 2 1+r - x^ 2 1-r =1 ; r 1 . Then S represents

Mathematics · JEE Main · NTA Exams — Co-ordinate Geometry

Let \(s=\left\{(x, y) \in R^{2}: \frac{y^{2}}{1+r}-\frac{x^{2}}{1-r}=1\right\} ; r \neq 1\). Then S represents

an ellipse whose eccentricity is \(\frac{1}{\sqrt{\mathrm{r}+\mathrm{l}}}\), where r > 1
a hyperbola whose eccentricity is \(\frac{2}{\sqrt{r+1}}\), when 0 < r < 1
a hyperbola whose eccentricity is \(\frac{2}{\sqrt{1-r}}\), when 0 < r < 1
an ellipse whose eccentricity is \(\sqrt{\frac{2}{r+1}}\), when r > 1

Answer

(C) a hyperbola whose eccentricity is 2 1-r , when 0 < r < 1

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