What is the locus of the equations `x^2+y^2+z^2=0`?

Name the locus of the equation x^2+y^2=0 .

Solve the following systems of homogenous equations: {:(x+2y-2z=0),(4x+y-3z=0),(5x-4y-9z=0):}

Use product : {:[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)] to solve the system of equations: x-y+2z=1,2y-3z=1,3x-2y+4z=2

Solve the following systems of homogenous equations: {:(3x+y-2z=0),(x+y+z=0),(x-2y+z=0):}

Using matrix method , solve the equations x-y+z=4 2x+y-3z =0 x+y+z=2