Question

The equation $\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0$ represents an ellipse, if ___________.

Answer 1

For given equation $\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0$
Represents an ellipse if
2 $-$ r < 0 and r $-$ 5 < 0
i.e r > 2 and r < 5
i.e 2 < r < 5