Question

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

• A. $r>2$
• B. $2<r<5$
• C. $r>5$
• D. $r=(2,5)$

Answer 1

Answer: (B)

$2<r<5$

Standard equation for ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0\Rightarrow \frac{x^2}{2-r}+\frac{y^2}{r-5}=-1\Rightarrow \frac{x^2}{r-2}+\frac{y^2}{5-r}=1$

for the above equation to be an ellipse $r-2>0\&5-r>0r>2\&r<5$

so $2<r<5$

so option B is correct