SOLUTION: Describe and find an equation for the shape generated by all points (x,y,z) that are two units from the point (4,-1,1). Please help me!!! Thanks

Algebra ->  Vectors -> SOLUTION: Describe and find an equation for the shape generated by all points (x,y,z) that are two units from the point (4,-1,1). Please help me!!! Thanks      Log On


   

Question 184987: Describe and find an equation for the shape generated by all points (x,y,z) that are two units from the point (4,-1,1). Please help me!!! Thanks
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The locus of points (x, y, z) that are 2 units from a given point (4, -1, 1) describe a sphere whose center is at (4, -1, 1) and whose radius is 2 units.
The general form for a sphere with center at (h, k, l) and radius (r) is given by:
%28x-h%29%5E2%2B%28y-k%29%5E2%2B%28z-l%29%5E2+=+r%5E2 so for this problem, you have the equation:
highlight%28%28x-4%29%5E2%2B%28y%2B1%29%5E2%2B%28z-1%29%5E2+=+4%29