# Visualizing a strange quadric surface

#### Woland

Hi all,

I am trying to visualize the following quadric surface:
x^2 + y^2 + z^2 = z

Could someone please help me understand what this surface looks like? I could not find an example of this one on the internet.

Thank you.

#### Hurkyl

Staff Emeritus
Gold Member
Do some algebra to simplify it. (e.g. things like collecting similar terms, completing the square, factoring, change of variable, etc)

#### maze

Consider what the surface
(x-a)^2 + (y-b)^2 + (z-c)^2 = d

looks like

#### Woland

(x-a)^2 + (y-b)^2 + (z-c)^2 = d is a sphere centered at a, b, c with radius square root of d.

Now regarding the first post, I can bring the z over to the left hand side:

x^2 + y^2 + z^2 - z = 0

Then complete the square

x^2 + y^2 + (z - 1/2)^2 -1/4 = 0
[(z - 1/2)^2 = z^2 - 2*1/2 z + 1/4]

Then

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

This means that this is a sphere centered at 0,0, 1/2. Is that correct?

#### mathman

This means that this is a sphere centered at 0,0, 1/2. Is that correct?
Yes and the radius is 1/2.

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