CALC 3 Q Help!! Reduce the equation to one of the standard forms and classify the surface.
x^2-y^2+z^2-2x+2y+4z+2=0

Question

CALC 3 Q Help!! Reduce the equation to one of the standard forms and classify the surface. 
x^2-y^2+z^2-2x+2y+4z+2=0

anonymous · Answer

complete the square for all variables.
$$x^2 - 2x = (x-1)^2 - 1$$$$y^2 + 2y = (y+1)^2 - 1$$$$z^2 + 4z = (z+2)^2 - 4$$
so we have$$(z+2)^2 = 4 - (x-1)^2 - (y+1)^2$$

solve for z = f(x,y)

let me know if i should keep going

anonymous · Answer

my bad it's 2y - y^2 = (1 - y)^2 - 1

anonymous · Answer

(x-1)^2-(y-1)^2+(z+2)^2=3 |dw:1381350287696:dw|

anonymous · Answer

i havent drawn surfaces in a while so it's probably best the way vijay has it, which is, not solving for z = f(x,y). that would be a useless step in the drawing process and probably identifying process

bgrg007 · Answer

i got (z+2)^2=4-(x-1)^2+(y-1)^2

anonymous · Answer

that is the right answer

bgrg007 · Answer

so im not going crazy. haha the answer i found on chegg was completely different so i was worried. also, the drawing @vvijay has would be a hyperboloid with 2 sheets?