Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0\Rightarrow \frac{x^2}{r-2}+\frac{y^2}{5-r}=1$ represents an ellipse $\Rightarrow r-2>0,5-r>0\Rightarrow r>2,r<5\Rightarrow 2<r<5$