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The radius of the circle passing through the points of intersection of ellipse fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1 and x2 – y2 = 0 is -

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  1. fraction numerator a b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction    
  2. fraction numerator square root of 2 a b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction    
  3. fraction numerator a to the power of 2 end exponent minus b to the power of 2 end exponent over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction    
  4. fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent over denominator square root of a to the power of 2 end exponent – b to the power of 2 end exponent end root end fraction    

    Answer:The correct answer is: fraction numerator square root of 2 a b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fractionTwo curves are symmetrical about both axes and intersect in four points, so, the circle through their points of intersection will have centre at origin.
    Solving x to the power of 2 end exponent minus y to the power of 2 end exponent = 0 and fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction= 1, we get
    x to the power of 2 end exponent equals y to the power of 2 end exponent = fraction numerator a to the power of 2 end exponent b to the power of 2 end exponent over denominator a to the power of 2 end exponent plus b to the power of 2 end exponent end fraction
    Therefore radius of circle
    =square root of fraction numerator 2 a to the power of 2 end exponent b to the power of 2 end exponent over denominator a to the power of 2 end exponent plus b to the power of 2 end exponent end fraction end root = fraction numerator square root of 2 a b over denominator square root of a to the power of 2 end exponent plus b to the power of 2 end exponent end root end fraction

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