Maths-
General
Easy

Question

The line among the following that touches the y to the power of 2 end exponent equals 4 a x is

  1. x plus m y plus a m cubed equals 0    
  2. x minus m y plus a m to the power of 2 end exponent equals 0    
  3. x plus m y minus a m squared equals 0    
  4. y plus m x plus a m to the power of 2 end exponent equals 0    

Hint:

The equation of tangent to parabola is given as y equals m x space plus space a over m with slope = m.
Similarly find the equation of tangent to parabola with slope = 1 over m and simplify.

The correct answer is: x minus m y plus a m to the power of 2 end exponent equals 0


     Condition 1
    The line with slope 'm' is a tangent to parabola  y to the power of 2 end exponent equals 4 a x
    The equation of tangent to parabola is given as y equals m x space plus space a over m (slope = m)
    Condition 2
    If slope = 1 over m , then equation of tangent
    rightwards double arrow y equals 1 over m x space plus space fraction numerator a over denominator begin display style bevelled 1 over m end style end fraction space equals space x over m space plus space m a

rightwards double arrow y equals space fraction numerator x space plus space m squared a over denominator m end fraction
rightwards double arrow y m space equals space x space plus m squared a
space

    Thus, equation of lines touching parabola with slope 1 over m is x minus m y plus a m to the power of 2 end exponent equals 0.

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