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Question

If f left parenthesis x right parenthesis is a decreasing function for all x element of R and f left parenthesis x right parenthesis greater than 0 for all x element of R then the range of K so that the equation fraction numerator x to the power of 2 end exponent over denominator f open parentheses K to the power of 2 end exponent plus 2 K plus 5 close parentheses end fraction plus fraction numerator y to the power of 2 end exponent over denominator f left parenthesis K plus 11 right parenthesis end fraction equals 1 represents an ellipse whose major axis is the X-axis is

  1. left parenthesis negative 2 , 3 right parenthesis  
  2. left parenthesis negative 3 , 2 right parenthesis  
  3.   
  4.  left parenthesis negative infinity comma negative 2 right parenthesis union left parenthesis 3 comma infinity right parenthesis  

The correct answer is: left parenthesis negative 3 , 2 right parenthesis


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