Question

how to find the shortest distance from the origin to the surface y^2-z^2=10 ?

Answer 1

d to the surface is given by \[d=\sqrt{x^2+y^2+z^2}\]if we minimize the distance we minimize its square, so we only need the absolute minimum of\[d(x,y,z)=x^2+y^2+z^2\]using substitution we can see that the surface allows us to eliminate one of the variables\[d(x,y,z)=x^2+y^2+(y^2-z^2)\]

Answer 2

I intend \(d(x,y,z)\) to represent the (square of the) distance function from the origin in case I didn't make that clear

Answer 3

oops, typo
also meant that\[d(,y,z)=x^2+y^2+(y^2-10)\]

Answer 4

shouldn't is be eliminate the x ?

Answer 5

why
I typed above wrong, I meant\[d(x,y)=x^2+y^2+(y^2-10)\]subbing for z
I don't see how to sub for x in this problem