Question

Find an equation of largest sphere with center(5,4,9) that is contained in the first octant.

Answer 1

Such a sphere can have a radius of up to 4, so that its equation would be

`(x-5)^2+(y-4)^2+(z-9)^2=16`

Any larger radius would make the sphere cross the plane
`y=0` and it would no longer be contained in the first octant.