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Easy

Question

If a tangent to the parabola 4y2 = x makes an angle of 60º with the x- axis, then its point of contact is-

  1. open parentheses fraction numerator 1 over denominator 48 end fraction comma fraction numerator 1 over denominator 8 square root of 3 end fraction close parentheses    
  2. open parentheses fraction numerator 3 over denominator 16 end fraction comma fraction numerator square root of 3 over denominator 8 end fraction close parentheses    
  3. open parentheses fraction numerator 1 over denominator 48 end fraction comma negative fraction numerator 1 over denominator 8 square root of 3 end fraction close parentheses    
  4. open parentheses fraction numerator 3 over denominator 16 end fraction comma negative fraction numerator square root of 3 over denominator 8 end fraction close parentheses    

hintHint:

find out the values of m and a and substitute their values.

The correct answer is: open parentheses fraction numerator 1 over denominator 48 end fraction comma fraction numerator 1 over denominator 8 square root of 3 end fraction close parentheses




    = (1/48, 1/8√3)

    m= tan(60) = 1.732
    a= 1/16
    point of contact = (a/m2, 2a/m)
    = (1/48, 1/8√3)

    point of contact = (a/m2, 2a/m)
    slope = tan ( angle made with the x axis)
    this gives us the value of m
    y^2 = x/4 = 4(1/16)x
    a = 1/16

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