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

A hyperbola whose eccentricity is \(\frac{2}{{\sqrt {1 + r} }}\), 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.

An ellipse whose eccentricity is \(\frac{1}{{\sqrt {r + 1} }}\), when r > 1.

Let \({\rm{S}} = \left\{ {\left( {x,y} \right) \in {{\rm{R}}^2}:\frac{

1.	Let \({\rm{S}} = \left\{ {\left( {x,y} \right) \in {{\rm{R}}^2}:\frac{{{y^2}}}{{1 + {\rm{r}}}} - \frac{{{x^2}}}{{1 - {\rm{r}}}} = 1} \right\}\), where r ≠ ±1. Then s represents:
A.	A hyperbola whose eccentricity is \(\frac{2}{{\sqrt {1 - r} }}\), when 0 < r < 1.
B.	An ellipse whose eccentricity is \(\sqrt {\frac{2}{{r + 1}}} \), when r > 1.
C.	A hyperbola whose eccentricity is \(\frac{2}{{\sqrt {1 + r} }}\), when 0 < r < 1.
D.	An ellipse whose eccentricity is \(\frac{1}{{\sqrt {r + 1} }}\), when r > 1.
Answer» C. A hyperbola whose eccentricity is \(\frac{2}{{\sqrt {1 + r} }}\), when 0 < r < 1.

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

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