x^2 +y^2 -z^2 = 0 --------(i)Originally Posted byAK713

Rearranging that,

x^2 +y^2 = z^2 ----------(ii)

The LHS of (ii) is a circle.

The RHS is a square of a z-coordinate. It could be the square of the radius of the LHS at the z-coordinate.

When z=0, the circle at the LHS is zero too, or no circle. It is (0,0,0), or the origin.

When z = 1, or z = -1, the circle at the LHS has a radius of 1.

When z = 2, or z = -2, the circle at the LHS has a radius of 2.

When z = 3, or z = -3, the circle at the LHS has a radius of 3.

Etc...

The figure then is that of a cone whose apex is at the (0,0,0) and opening upwards, and that of its mirror-shape that opens downward.

That is if the z-axis is the usual up-down or vertical axis in the x,y,z axes setup.