Question

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

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

Answer 1

The correct option is B $2<r<5$

Given $\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0$ represents a ellipse

$⟹\frac{x^2}{2-r}+\frac{y^2}{r-5}=-1$

$⟹\frac{x^2}{r-2}+\frac{y^2}{5-r}=1$

Since this equation is an ellipse so $r-2>0,5-r>0⟹2<r<5$