Equation of sphere given 3 pointcalc 3

[memish]

Homework Statement

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

Homework Equations

Not sure...i used the distance formula though

The Attempt at a Solution

This class has just started and i have no idea where to start with this because 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


Please help! I am really frustrated =(

 

[rock.freak667]

Homework Equations

Not sure...i used the distance formula though

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

 

[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.

 

[memish]

thanks, rockfreak

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

 

[memish]

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

 

[njama]

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

The equation would be:

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