# What is the standard equation of a sphere?

• February 22nd 2011, 08:07 PM
thyrgle
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?
• February 22nd 2011, 08:11 PM
pickslides
$x^2+y^2+z^2 = r^2$

is a sphere centred at the origin with radius $r$
• February 22nd 2011, 08:14 PM
thyrgle
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 "?"?
• February 22nd 2011, 08:51 PM
Prove It
Any letter can be used... I would probably use something close to $\displaystyle k$...

Many texts write the standard equation for a sphere as

$\displaystyle (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2$
• February 22nd 2011, 08:54 PM
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.
• February 22nd 2011, 08:55 PM
Prove It
See my edit...
• February 22nd 2011, 10:00 PM
Wilmer
• February 23rd 2011, 03:14 AM
HallsofIvy
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?
• February 23rd 2011, 11:59 AM
pickslides
Quote:

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.