Maths-
General
Easy

Question

The line x + my + n = 0 will be a tangent to the parabola y2 = 4ax if

  1. mn = al 2    
  2. m = an2    
  3. n= am2    
  4. am = n2    

The correct answer is: n= am2


    To find the condition for which the equation is tangent to parabola.
    Given,  x + my + n = 0
    y = fraction numerator negative x minus n over denominator m end fraction
    given, y squared = 4ax
    Therefore, open parentheses fraction numerator negative x minus n over denominator m end fraction close parentheses squared = 4ax.
    x squared plus left parenthesis 2 n minus 4 a m squared right parenthesis x plus n squared equals 0
    If the line is to be tangent, b squared minus 4 a c equals 0
    left parenthesis 2 n minus 4 a m squared right parenthesis minus 4 n squared equals 0
    a m squared left parenthesis a m squared minus n right parenthesis equals 0
a m squared minus n equals 0
n equals a m squared

    Therefore, for the equation to be tangent to parabola, n equals a m squared.

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