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Let S={(x,y) in R^(2):(y^(2))/(1+r)-(x^(...

Let `S={(x,y) in R^(2):(y^(2))/(1+r)-(x^(2))/(1-r)=1}`, where `r ne pm 1`. Then S represents:

A

A hyperbolawhose eccentricity is `(2)/(sqrt(r+1))`, where `0 lt r lt 1`.

B

An ellipse whose eccentricity is `(1)/(sqrt(r+1)), " where" r gt 1`

C

A hyperbola whose eccentricity is `(2)/(sqrt(1-r)), " where " 0 lt r lt 1`.

D

An ellipse whose eccentricity is `sqrt((2)/(r+1)), " where " r gt 1`.

Text Solution

Verified by Experts

The correct Answer is:
D
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