# Two Parabola Problems

1. May 14, 2014

### varunKanpur

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

2. May 14, 2014

### Simon Bridge

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 $p=(p_x,p_y): p_x\neq 0$

3. May 14, 2014

### varunKanpur

I got the #1 problem, I was making it more lengthy.

4. May 14, 2014

### Simon Bridge

OK - so what about #2?
Same suggestions.