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The equatio (x ^(2 ))/( 2 -r) + (y ^(2))...

The equatio `(x ^(2 ))/( 2 -r) + (y ^(2))/(r -5) +1=0` represents an ellipse, if

A

`(-oo,2)cup (5, oo)`

B

(2, 5)

C

(5, 10)

D

`(-oo, 1)`

Text Solution

Verified by Experts

The correct Answer is:
B
The given equation can reduces to
`(x^(2))/(2-r)+(y^(2))/(r-5)= -1 rArr (x^(2))/(r-2)+(y^(2))/(5-r)=1`
For ellipse, `(x^(2))/(a^(2)) +(y^(2))/(b^(2))=1, a^(2),b^(2) gt 0`
`rArr r-2 gt 0, 5-r gt 0 rArr r gt 2, r lt 5 rArr 2 lt r lt 5`
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