I am not able to solve the following problem(adsbygoogle = window.adsbygoogle || []).push({});

#1) Prove that the normal to parabola y^{2}=4ax at (am^{2},-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 y^{2}=4ax from a point , not on the y-axis, will be normals to the parabola x^{2}=4y?

I have no idea on how to solve this question

Thanks in Advance

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# Two Parabola Problems

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