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

Let z=3x^{2}-y^{2}. Find all points at which ||∇Z||=6

First things first

I took the partials dz/dx and dz/dy

dz/dx=6x

dx/dy=-2y

I know that √(36x^{2}+4y^{2})=6 or (36x^{2}+4y^{2})=36

Then using the above relation I solved for each variable getting

1.y=√(9-x^{2})

2.x=√(1-1/9y^{2})

We already have the relation from the partials

A.-2y=0

B.6x=0

So I plugged in 1 into A and 2 into B to get the following

x=+-1 and y=+-3

However the answers don't check out

Where did I go wrong?