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x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1 will repr...

`x^2/(r^2-r-6)+y^2/(r^2-6r+5)=1` will represent ellipse if r lies in the interval

A

`(-oo,-2)`

B

`(3,-oo)`

C

`(5,oo)`

D

`(1,oo)`

Text Solution

Verified by Experts

`r^(2)-r-6lt 0 and r^(2)-6r+lt0`
or `(r-3)(r+2)lt 0 and (r-1)(r-5)gt=0`
`or (rlt-2 or rgt) and (rlt or gt5)`
i.e., `rlt-2 or r gt5`
Also, `r^(2)-r-6ne r^(2)-6r+5`
`or ne(11)/(5)`
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