Question

How do I determine the type of quadric surface for an equation like this? x^2 + 2y^2 + 4z^2 - 4z + 1 = 0

Answer 1

this is a sphere equation..

Answer 2

\[(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=r^2\]

Answer 3

you sure about eq. because r=0

Answer 4

http://www.wolframalpha.com/input/?i=plot+sqrt%28-x^2-2y^2%29%2F2%2B1%2F2

Answer 5

i've figured it out, there is only 1 solution to the equation which is (0,0,1/2), which means the equation is a single point. thanks anyway!

Answer 6

you mean real solution..

Answer 7

it is clear..\[x^2+2y^2+(2z-1)^2=0\]