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For the ellipse fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma the foci are

  1. ( ±1, 0)    
  2. (0, ± 1)    
  3. open parentheses plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction comma 0 close parentheses    
  4. open parentheses plus-or-minus fraction numerator 1 over denominator 2 end fraction comma 0 close parentheses.    

Hint:

To find focii, find the eccentricity by the formula
e = square root of 1 space minus space b squared over a squared end root

The correct answer is: ( ±1, 0)


     Given : Equation of ellipse
    fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma
    Center of ellipse = (h, k) = (0,0)
    Eccentricity (e) =square root of 1 space minus space b squared over a squared end root
    rightwards double arrowe =square root of 1 space minus space 1 half end root space equals space fraction numerator 1 over denominator square root of 2 end fraction
    rightwards double arrowFoci = ( h plus-or-minusae , k)
    where a = square root of 2
    rightwards double arrowFoci = ( 0 plus-or-minus square root of 2 cross times fraction numerator 1 over denominator square root of 2 end fraction , 0)
    rightwards double arrowFoci = ( 0 plus-or-minus 1 , 0)
    rightwards double arrowFoci = (plus-or-minus 1 , 0)

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