Question

If $f ( x )$ is a continuous decreasing function then the set of values of $k$ for which the major axis of the ellipse $\frac{ x ^2}{ f \left( k ^2+2 k +5\right)}+\frac{ y ^2}{ f ( k +11)}=1$ is the $x$ axis, is equal to

• A. $k \in(-2,3)$
• B. $k \in(-3,2)$
• C. $k \in(-\infty,-3) \cup(2, \infty)$
• D. $k \in(-\infty,-2) \cup(3, \infty)$

Answer 1

Answer: (B)

$\because f ( x )$ is a continuous decreasing function and major axis to be $x$ axis
$\therefore f \left( k ^2+2 k +5\right)> f ( k +11) $
$\Rightarrow k ^2+2 k +5< k +11$
$\Rightarrow k ^2+ k -6<0 $
$\Rightarrow( k +3)( k -2)<0$
$\Rightarrow k \in(-3,2)$