# Equation of sphere given 3 pointcalc 3

1. Sep 12, 2009

### memish

1. The problem statement, all variables and given/known data
Find the equation of a sphere that contains the points (-3,0,0) (3,4,4) and (-4,3,4) if its center lies on the xz plane

2. Relevant equations
Not sure...i used the distance formula though

3. The attempt at a solution
This class has just started and i have no idea where to start with this becuase this is our first homework!! I am trying to find a point equidistant from all three points that could be the center, but I could only find a plane which I found to be 2z+3x=4

2. Sep 13, 2009

### rock.freak667

General of a sphere

(x-h)2+(y-j)2+(z-k)2=r2 where (h,j,k) is the centre of the sphere.

you have three points and what plane the centre lies on

3. Sep 13, 2009

### lkh1986

This question is like an analogy to those involving simultaneous equations. ;) Try to substitute the 3 points into the general equations and solve for the unknowns.

4. Sep 13, 2009

### memish

thanks, rockfreak

lkh - what do you mean by the problems with simultaneous equations?

5. Sep 13, 2009

### memish

ohhh ok thanks!!! i got it it was much simpler than i thought :)

6. Sep 13, 2009

### njama

Because the center lies on the xz plane than its coordinates are (x,0,z)

The equation would be:

$$(x-x_0)^2+y^2+(z-z_0)^2=r^2$$