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?