Maths-
General
Easy

Question

In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is square root of 10 minus square root of 5 The equation of the ellipse

  1. fraction numerator x to the power of 2 end exponent over denominator 36 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 18 end fraction equals 1    
  2. fraction numerator x to the power of 2 end exponent over denominator 40 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 20 end fraction equals 1    
  3. fraction numerator x to the power of 2 end exponent over denominator 20 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 10 end fraction equals 1    
  4. fraction numerator x to the power of 2 end exponent over denominator 10 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1    

The correct answer is: fraction numerator x to the power of 2 end exponent over denominator 10 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 5 end fraction equals 1


    a e equals b rightwards double arrow e to the power of 2 end exponent equals fraction numerator b to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction rightwards double arrow e to the power of 2 end exponent equals 1 minus e to the power of 2 end exponent therefore e equals fraction numerator 1 over denominator square root of 2 end fraction text  also  end text S A equals a minus a e equals square root of 10 minus square root of 5
    therefore a open parentheses 1 minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses equals square root of 10 open parentheses 1 minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses therefore a to the power of 2 end exponent equals 10 rightwards double arrow b to the power of 2 end exponent equals 5

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