EllipseHardBloom L3
Question
If $\frac{x^{2}}{f(4a)} + \frac{y^{2}}{f\left( a^{2} - 5 \right)} = 1$ represents an ellipse with major axis as $y$-axis and $f$ is a decreasing function, such that $f(x) > 0.\forall x \in R$, then complete set of values of $a$ is :
Options
A.$( - \infty,1)$
B.$( - \infty, - 1) \cup (5,\infty)$
C.$( - 1,4)$
D.$( - 1,5)$
Solution
Sol.(d) $0 < f(4a) < f\left( a^{2} - 5 \right)$
$${\Rightarrow \ 4a > a^{2} - 5 }{\Rightarrow (a - 5)(a + 1) < 0 }{\Rightarrow \ a \in ( - 1,5)}$$
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