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Two Parabola Problems

  1. May 14, 2014 #1
    I am not able to solve the following problem

    #1) Prove that the normal to parabola y2=4ax at (am2,-2am) intersects the parabola again at an angle tan-1(m/2)

    What I am thinking is to solve the equation of parabola and equation of normal y=mx-am-3-2am simultaneously and at that point I will find the slope of tangent and will get the angle between tangent and normal. The problem is that answer is not coming.

    #2) For what values of a will the tangents drawn to parabola y2=4ax from a point , not on the y-axis, will be normals to the parabola x2=4y?

    I have no idea on how to solve this question
    Thanks in Advance
     
  2. jcsd
  3. May 14, 2014 #2

    Simon Bridge

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    Start with the first one to begin with.

    Please show your working?
    Show each step with your reasoning.
    It can hep to reverse the roles of the x and y axes.

    The key to the second one is to rewrite the problem statement in maths.
    i.e. a point not on the y axis is point ##p=(p_x,p_y): p_x\neq 0##
     
  4. May 14, 2014 #3
    I got the #1 problem, I was making it more lengthy.
     
  5. May 14, 2014 #4

    Simon Bridge

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    OK - so what about #2?
    Same suggestions.
     
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