Find an equation of the largest sphere with center (10, 6, 4) that is contained completely in the first octant.

(x-10) ² + (y-6) ² + (z-4) ² = 16

Step-by-step explanation:

The largest sphere contained in the first octant can only have a radius equal to the shortest distance from the center to the coordinates planes.

(10, 6, 4).

For the coordinate x the distance to the plane y-z is 10

For the coordinate y the distance to the plane x-z is 6

For the coordinate x the distance to the plane x-y is 4

So the maximum radius contained is r=4.

For the formula of sphere:

(x-10) ² + (y-6) ² + (z-4) ² = r²

we replace the r.