Maths-
General
Easy

Question

The eccentricity of the curve represented by the equation x to the power of 2 end exponent plus 2 y to the power of 2 end exponent minus 2 x plus 3 y plus 2 equals 0 is

  1. 0    
  2. 1/2    
  3. 1 divided by square root of 2    
  4. square root of 2    

The correct answer is: 1 divided by square root of 2


    Equation x to the power of 2 end exponent plus 2 y to the power of 2 end exponent minus 2 x plus 3 y plus 2 equals 0 can be written as
    fraction numerator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent over denominator 2 end fraction plus open parentheses y plus fraction numerator 3 over denominator 4 end fraction close parentheses to the power of 2 end exponent equals fraction numerator 1 over denominator 16 end fractionÞfraction numerator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent over denominator left parenthesis 1 divided by 8 right parenthesis end fraction plus fraction numerator open parentheses y plus fraction numerator 3 over denominator 4 end fraction close parentheses to the power of 2 end exponent over denominator left parenthesis 1 divided by 16 right parenthesis end fraction equals 1,
    which is an ellipse with a to the power of 2 end exponent equals fraction numerator 1 over denominator 8 end fraction and b to the power of 2 end exponent equals fraction numerator 1 over denominator 16 end fraction
    therefore fraction numerator 1 over denominator 16 end fraction equals fraction numerator 1 over denominator 8 end fraction left parenthesis 1 minus e to the power of 2 end exponent right parenthesis Þe to the power of 2 end exponent equals 1 minus fraction numerator 1 over denominator 2 end fractionÞe equals fraction numerator 1 over denominator square root of 2 end fraction.

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