Question

calc 3 help

find points on the surface xy-z^2=1 that are closest to the origin

Answer 1

so far, I've solved for z^2, and found g(x, y), which I plugged z^2 into and got

g( x, y) = x^2+y^2+xy-1

Answer 2

then from there, found that x and y are both 0, and when I plugged in those values into the original equation I got -z^2=1

which is where I'm currently stuck on

Answer 3

well d^2= x^2+y^2+xy=1 then you solve for dg/dx = 2x+y=0 and dg/dy=2y+x=0 then you solve so you get x=0 and y=0 but when you plug it into the original equation xy-z^2=1 you get z^2 = -1 which doesn't work