# Thread: What is the standard equation of a sphere?

1. ## What is the standard equation of a sphere?

I can find the ellipsoid, paraboloid, and hyperboloid standard equation but, all I can find out about the sphere is the volume. It doesn't even mention the equation on wikipedia: Sphere - Wikipedia, the free encyclopedia. Does anyone know the standard equation for it?

2. $x^2+y^2+z^2 = r^2$

is a sphere centred at the origin with radius $r$

3. Cool thanks for the quick reply, one more thing, for (x-h)^2 + (x-k)^2 (z-?)^2 = r^2 what would be the typical letter for the "?"?

4. Any letter can be used... I would probably use something close to $\displaystyle k$...

Many texts write the standard equation for a sphere as

$\displaystyle (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2$

5. @Prove It: So there is no typically accepted way? Ok, then thanks. Just wondering because, I know, for example, that y = mx + b can be substituted with any letters but, by convention we use y, m, x, and b.

6. See my edit...

7. Whether you write the equation as $(x- a)^2+ (y- b)^2+ (z- c)^2= r^2$ or $(x- h)^2+ (y- k)^2+ (z- j)^2= r^2$ or $(x- x_0)^2+ (y- y_0)^2+ (z- z_0)^2= r^2$ you should include the information that the point (a, b, c) (or (h, k, j) or [itex](x_0, y_0, z_0) is the center of the circle and that r is the radius.

You say you found the equations for ellipsoid, paraboloid, and hyperboloid (of one or two sheets?). What convention did they use for the center?

8. Originally Posted by thyrgle
@Prove It: So there is no typically accepted way? Ok, then thanks. Just wondering because, I know, for example, that y = mx + b can be substituted with any letters but, by convention we use y, m, x, and b.
In Mathematics you will find letters at the beginning of the alphabet a,b,c,etc represent constants while at the other end x,y,z represent variables.

With the case y=mx+b the m represents the gradient which is a special type of constant.