Can this be graphed?

Question

Original equation given to graph is:
z = √(x^2 + y^2)

I squared both sides to get:
z^2 = x^2 + y^2

I subtract z^2 from both sides to get all variables on the same side and I get:
x^2 + y^2 - z^2 = 0

Can this be graphed? I'm wanting to answer this question as the graph "DNE" (does not exist). Is that right, or am I totally missing something here?
If I did traces, the equations would all still equal zero ...
So would this 'graph' then just be a point (the origin) instead of DNE?

Thank you for your time and help. :)

Answer 1

The graph of this equation is a pair of cones with vertices at the origin and a central axis on the z axis. One opens as z goes positive, and the other opens as z goes negative. A 2-dimensional plot in the xz or yz planes is an X. In the xy plane, there will only be a dot at the origin, which is why you get DNE on your graphing calculator.

Answer 2

Actually, back up one step...

z^2 = x^2 + y^2 is the formula for a circle with radius z and center (0,0).

The general circle formula is
r^2 = (x-a)^2 + (y-b)^2
where r=radius, and (a,b) is the center of the circle.

(Do you have a value for z?? If not, you probably can't graph it.)