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. $2>\lambda >5$

Answer 1

Answer: (B)

$\lambda <2$

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

So both denominators should be positive as they are squares.

In the given equation $\frac{x^2}{2-\lambda }-\frac{y^2}{\lambda -5}-1=0$

So, $2-\lambda >0,$ $-(\lambda -5)>0$

$\Rightarrow \lambda <2,\lambda <5$

$\Rightarrow \lambda <2$

as it satisfies both condition $\lambda <2,\lambda <5$