Q. If $\frac{x^{2}}{f(4a)} + \frac{y^{2}}{f(a^{2} - 5)}$ represents an ellipse with major axis as $y$-axis and $f$ is a decreasing function, then
A) $a \in ( - \infty,\ 1)$
B) $a \in (5,\ \infty)$
C) $a \in (\ 1,\ 4)$
D) $a \in ( - 1,5)$
Explanation
(d)
Since, $y$-axis is major axis
$\Rightarrow f(4a) < f(a^{2} - 5)$
$\Rightarrow 4a > a^{2} - 5$ ($\because f$ is decreasing)
$\Rightarrow a^{2} - 4a - 5 < 0$
$\Rightarrow a \in ( - 1,\ 5)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.