Vectors and Spheres

Question

Find an equation of the largest sphere with center (8,10,4) that is contained completely in the first octant.

If you can explain the steps that you took to solve this, it would help a lot.

Answer 1

(x-8)^2 + (y-10)^2 + (z-4)^2 = r^2 = 4^2 r=smallest x,y or z coordinate of the center, in order to stay inside the 1st octant

same with just 2 dimensions, which is much easier to visualize or graph

(x-8)^2 + (y-4)^2 = 4^2 is a circle that stays within the 1st quadrant

center (8,4) radius = 4= smallest x or y coordinate of the center