(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the points (x,y,z) on the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface is the line from the origin to the point (x,y,z).

2. Relevant equations

normal line means take the gradient, <∂F/∂x, ∂F,∂y, ∂F,∂z>, and evaluate at the point

3. The attempt at a solution

n= -2xi+ -2yj+ 1k, wherei=(1 0 0)^{T},j=(0 1 0)^{T},k=(0 0 1)^{T}.

So we want an (x,y,z) that such that the normal vectornis a scalar multiple of xi+ yj+ (z=x^{2}+y^{2}+1)k.

<-2x,-2y,1> = ß<x,y,x^{2}+y^{2}+1>

<-2,-2,0> = <ß, ß, ß(x^{2}+y^{2})>

Am I doing this right? Something ain't working.

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# Homework Help: Points where normal at point on surface equals line from origin to that point

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