Question

If $\frac{x^2}{a^2-5}+\frac{y^2}{4a}=1$ represents an ellipse with major axis on $y-$axis, then:

• A. $a\in (\sqrt{5},5)$
• B. $a\in (-1,\sqrt{5})\cup (\sqrt{5},5)$
• C. $a\in (-1,5)$
• D. $a\in (0,5)$

Answer 1

The correct option is A $a\in (\sqrt{5},5)$

$a>0$ and $a^2-5>0$
$⟹a>\sqrt{5}$
y-axis is major axis
so $4a>a^2-5$
$⟹a^2-4a-5<0$
$⟹a$ belongs to ($1,5)$
So taking intersection $a$ belongs to $(\sqrt{5},5)$