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Equation of one of the common tangent of y2 = 4x and fraction numerator x to the power of 2 end exponent over denominator 4 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 3 end fraction equals 1 is equal to-

  1. x + 2y + 4 = 0    
  2. x + 2y – 4 = 0    
  3. x – 2y – 4 = 0    
  4. None of these    

hintHint:

find out tangents of curves in slope form and equate the constant terms.

The correct answer is: x + 2y + 4 = 0


    x+ 2y+4 =0


    Equation of tangent to the parabola in slope form is:
    y = mx + 1/m
    Equation of tangent to the ellipse in slope form is :
    y = mx + √(a2m2+b2)

    here, √(a2m2+b2) = 1/m
    on squaring both sides, we get
    4m2+3 = 1/m2
    4m4+3m2-1=0
    m2 = -1, ¼
    m= ½ or -1/2  when m2= 1/4


    equation of tangent :
    y=x/2 + 2=> 2y=x+4
    y= -x/2 -2 => 2y=-x -4=> x+ 2y+4 =0

    a common tangent is a line that is a tangent to more than one curves..

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