If f ( x ) is a continuous decreasing function then the set of values of k for which the major axis of the ellipse ( x 2/ f ( k 2+2 k +5))+( y 2/ f ( k +11))=1 is the x axis, is equal to

Question

If f ( x ) is a continuous decreasing function then the set of values of k for which the major axis of the ellipse ( x 2/ f ( k 2+2 k +5))+( y 2/ f ( k +11))=1 is the x axis, is equal to (A) k ∈(-2,3) (B) k ∈(-3,2) (C) k ∈(-∞,-3) ∪(2, ∞) (D) k ∈(-∞,-2) ∪(3, ∞)

Tardigrade Admin · Accepted Answer

∵ f ( x ) is a continuous decreasing function and major axis to be x axis ∴ f ( k 2+2 k +5)> f ( k +11) ⇒ k 2+2 k +5< k +11 ⇒ k 2+ k -6<0 ⇒( k +3)( k -2)<0 ⇒ k ∈(-3,2)

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

$k \in (- 2, 3)$

$k \in (- 3, 2)$

$k \in (- \infty, - 3) \cup (2, \infty)$

$k \in (- \infty, - 2) \cup (3, \infty)$

$∵ f (x)$ is a continuous decreasing function and major axis to be $x$ axis
$∴ f (k^{2} + 2 k + 5) > f (k + 11)$
$\Rightarrow k^{2} + 2 k + 5 < k + 11$
$\Rightarrow k^{2} + k - 6 < 0$
$\Rightarrow (k + 3) (k - 2) < 0$
$\Rightarrow k \in (- 3, 2)$

Q. If f(x) is a continuous decreasing function then the set of values of k for which the major axis of the ellipse f(k2+2k+5)x2​+f(k+11)y2​=1 is the x axis, is equal to

k∈(−2,3)

k∈(−3,2)

k∈(−∞,−3)∪(2,∞)

k∈(−∞,−2)∪(3,∞)