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

Consider the ellipse `(x^(2))/(f(k^(2)+2k+5))+(y^(2))/(f(k+11))=1`,f(x) is a positive decreasing function the number of integral values of k for which the major axis is x -axis is

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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,)

Consider the ellipse x^2/(f(k^2-4k+6))+y^2/(f(k+12))=1 where f(x) is a positive decreasing function. The number of integral non-negative values of k for which major axis lies on the line y = 0 is

Knowledge Check

  • If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

    A
    4
    B
    3
    C
    2
    D
    1

  • If (x^2)/( f(4a)) +(y^2)/(f(a^2 -5)) represents an ellipse with major axis as y-axis and f is a decreasing function, then a belongs to :

    A
    `(1,4)`
    B
    `(-1,1)`
    C
    `(-1,5)`
    D
    `(5,oo)`

  • If (x^(2))/(f(4a)) +(y^(2))/(f(a^(2)-5)) represents an ellipse with major axis as y-axis and f is a decreasing function, then:

    A
    `a in (-oo, 1)`
    B
    `a in (5, oo)`
    C
    `a in (1, 4)`
    D
    `a in (-1, 5)`

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