Question

If $\frac{x^2}{f\left(4a\right)}+\frac{y^2}{f(a^2-5)}=1$ 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. $a\in (-1,5)$

Answer 1

The correct option is D

$a\in (-1,5)$

Since y-axis is major axis
$\Rightarrow f\left(4a\right)<f(a^2-5)\Rightarrow 4a>a^2-5(\because \text{f is decreasing})\Rightarrow a^2-4a-5<0\Rightarrow a\in (-1,5)$