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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 the ellipse if r lies in the interval

A

`(-oo,-2)`

B

`(3,-oo)`

C

`(5,oo)`

D

`(1,oo)`

Text Solution

AI Generated Solution

To determine the values of \( r \) for which the equation \[ \frac{x^2}{r^2 + r - 6} + \frac{y^2}{r^2 - 6r + 5} = 1 \] represents an ellipse, we need to ensure that both denominators are positive. This leads us to the following inequalities: ...
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