# #P# is a point on the parabola #x=t#, #y=t^2/2#. #A(4,1)# is a fixed point. As #P# varies, find the minimum distance of #P# from #A# and prove that for this position of #P#, #AP# is normal to the parabola?

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Thanks!

Thanks!

##### 1 Answer

Nov 20, 2017

The variable distance

Differentiating w r to t we get

Imposing the condition of minimum

At this position the coordinates of

At this stage the slope of

Now the equation of the parabola

So

Hence **slope of the normal** at