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Consider the ellipse (x^2)/(f(k^2+2k+5))...

Consider the ellipse `(x^2)/(f(k^2+2k+5))+(y^2)/(f(k+11))=1.` If `f(x)` is a positive decr4easing function, then the set of values of `k` for which the major axis is the x-axis is `(-3,2)dot` the set of values of `k` for which the major axis is the y-axis is `(-oo,2)dot` the set of values of `k` for which the major axis is the y-axis is `(-oo,-3)uu(2,oo)` the set of values of `k` for which the major axis is the y-axis is `(-3,-oo,)`

A

the set of values of k for which the major axis is the x-asix is (-3,2)

B

the set of values of k for which the major axis is the x-asix is `(-oo,2)`

C

the set of values of k for which the major axis is the x-asix is `(-oo,-3)uu(2,oo)`

D

the set of values of k for which the major axis is the x-asix is `(-3,oo)`

Text Solution

Verified by Experts

f(x) is a decreasing function and for the major axis to the a-axis
`f(k^(2)+2k)+5)gtf(k_11)`
or `k^(2)+2k+5ltk+11`
`or k in (-3,2) `
Then for the remaining values of k, i.e.,` k in (-oo,-3) uu(2,oo)`, the major axis is the y-axis
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