Q. The equation $\frac{x^{2}}{2 - \lambda}–\frac{y^{2}}{\lambda - 5\ } - 1 = 0$, represent an ellipse, if
A) $\lambda > 5$
B) $\lambda < 2$
C) $2 < \lambda < 5$
D) $2 > \lambda > 5$
Explanation
(b)
Given equation can be rewritten as
$\frac{x^{2}}{2 - \lambda} + \frac{y^{2}}{- \lambda + 5} = 1$
To represent an ellipse,
$2 - \lambda > 0$ and $–\lambda + 5 > 0$
$\Rightarrow \ \ \lambda < 2$ and $\lambda < 5$
$\Rightarrow \ \ \lambda < 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.