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:

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