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1. The problem statement, all variables and given/known data

Find an equation for the tangent plane to the surface z^2 = x^2 + 2y^2 at the point P = (1,2,3). Which other points on the surface have the same tangent plane?

2. The attempt at a solution

I find the derivatives:

f_{x}= x/(2*sqrt(x^2 + 2y^2))

f_{y}= 2y/(2*sqrt(x^2 + 2y^2))

The plane is given by:

z - f(1,2,3) = f_{x}(1,2,3)(x-1) + f_{y}(1,2,3)(y-2)

6z = 2x + 8y

So then, which other points on the surface have the same tangent plane?

I also have another question: Why does it suffice to write z = sqrt(x^2 + sy^2) instead of z = (+/-)sqrt(x^2 + sy^2) ?

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# Homework Help: Tangent plane to surface

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