Maths-
General
Easy

Question

The distance between the origin and the normal to the curve y = e2x + x2 at the point x = 0 is :

  1. square root of 3    
  2. fraction numerator 1 over denominator square root of 3 end fraction    
  3. fraction numerator 2 over denominator square root of 5 end fraction    
  4. none of these    

The correct answer is: fraction numerator 2 over denominator square root of 5 end fraction


    The point on the curve corresponding to x = 0 is (0, 1)[because y = e2x + x2 ]
    fraction numerator d y over denominator d x end fraction equals 2 e to the power of 2 x end exponent plus 2 x
    At (0, 1), fraction numerator d y over denominator d x end fraction equals 2 plus 0 equals 2
    Normal at (0, 1) is y minus 1 equals negative fraction numerator 1 over denominator 2 end fraction left parenthesis x minus 0 right parenthesis
    2y − 2 = − x
    x + 2y − 2 = 0
    Distance of (0, 0) from the normal equals fraction numerator 2 over denominator square root of 1 plus 4 end root end fraction equals fraction numerator 2 over denominator square root of 5 end fraction

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