Question

(1 point) Find an equation of the largest sphere with center (5,3,5)(5,3,5) and is contained in the first octant. Be sure that your formula is monic. Equation:

Answer 1

x^2+y^2+z^2-10x-6y-10z +50 =0

Explanation:

Given that a sphere is contained in the first octant

Centre of the sphere is given as (5,3,5)

Since this is contained only in the first octant radius should be at most sufficient to touch any one of the three coordinate planes

When it touches we can get the maximum sphere

We find that y coordinate is the minimum of 3 thus radius can be atmost 3 so that then only it can touch y =0 plane i.e. zx plane without crossing to go to the other octants.

Hence radius =3

Equation of the sphere would be

`(x-5)^2 +(y-3)^2+(z-5)^2 = 3^2\\x^2+y^2+z^2-10x-6y-10z +50 =0`