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Question

The line x = at2 meets the 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 equals 1 in the real points if

  1. |t| < 2    
  2. |t| ≤ 1    
  3. |t| > 1    
  4. None of these    

hintHint:

put the value of x into the equation of ellipse to get the value of y . find out the condition in which y becomes real

The correct answer is: |t| ≤ 1



    |t|<=1


    When x=at2, t4 + y2/b2=1 ,
    y2= (1-t4)b2
    y=±√(1-t4)b2 = ±b√(1-t4)
    for  y to be real, 1-t4>=0
    |t|<=1

    the term has to be greater than or equal to 0 inside the square root in order for the expression to give real values.

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