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The equation (x^2)/(1-r)-(y^2)/(1+r)=1,r...

The equation `(x^2)/(1-r)-(y^2)/(1+r)=1,r >1,` represents an ellipse (b) a hyperbola a circle (d) none of these

A

an ellipse

B

a hyperbola

C

a circle

D

None of these

Text Solution

Verified by Experts

Given equation is `(x^(2))/(1-r)-(y^(2))/(1+r)=1, " where "|r| lt 1`
`rArr 1-r " is (+ve) " and 1+r " is (+ve)" `
` therefore " Given equation is of the form "(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`.
Hence, it represents a hyperbola when `|r| lt 1`
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