Question

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

Answer 1

(x−10)²+ (y−6)²+ (z−4)²= 16

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.