Question

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

• A. $\lambda <5$
  
• B. $\lambda <2$
  
• C. $2<\lambda <5$
  
• D. $\lambda <2$ or < 5

Answer 1

The correct option is C $2<\lambda <5$


$\frac{x^2}{2-\lambda }+\frac{y^2}{\lambda -5}+1=0$
$\Rightarrow \frac{x^2}{\lambda -2}+\frac{y^2}{5-\lambda }=1$
To represent the equation of ellipse, we have:
$\lambda -2>0$
$\Rightarrow \lambda >2$
and
$5-\lambda >0$
$\Rightarrow 5<\lambda$
$\therefore 2<\lambda <5$