Under what condition does the equations `x^2+y^2+z^2+2ux+2uy+2w+d=0` represent a real sphere?

What does this equation x^2 - 4y^2 - 2x + 16y - 40 =0 represent?

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

The equation x^(2) + y^(2) + z^(2) = 0 represents

Under what condition do the equation kx-y=2and6x-2y=3 have a unique solution?

What should be the value of k for which the equation 3x^2+2y^2+(k+1)z^2+x-y+z=0 represents the sphere?

What should be the value of k for which the equation 3x^2+3y^2+(k+1)z^2+x-y+z=0 represents the sphere

The equation (x+y)^(2)-(x^(2)+y^(2))=0 represents

a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0 Under what condition the above equations represent infinitely many solution.