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Question

The eccentricity of the conic 3x2 + 4y2 = 24 is

  1. fraction numerator 1 over denominator 4 end fraction    
  2. fraction numerator 7 over denominator 4 end fraction    
  3. fraction numerator 1 over denominator 2 end fraction    
  4. square root of fraction numerator 7 over denominator 4 end fraction end root    

hintHint:

Formula for eccentricity(e)
e space equals space square root of 1 minus b squared over a squared end root

The correct answer is: fraction numerator 1 over denominator 2 end fraction


     Given : 
    3 x squared space plus space 4 y squared space equals space 24
    Dividing by 24 on both sides , we get
    rightwards double arrow x squared over 8 space plus space y squared over 6 space equals 1
    On comparing with general form x squared over a squared space plus space y squared over b squared space equals 1
    a squared space equals space 8 space a n d space b squared space equals 6
    Formula for eccentricity(e)
    e space equals space square root of 1 minus b squared over a squared end root
    Substituting the values,
    rightwards double arrow e space equals space square root of 1 minus 6 over 8 end root
rightwards double arrow e space equals space square root of 2 over 8 end root
rightwards double arrow e space equals space 1 half
    Thus, The eccentricity of the conic 3 x squared space plus space 4 y squared space equals space 24
 is 1 half

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