Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and radius of this sphere.

This is a sphere with a center    and radius

Step-by-step explanation:

Given that: (x,y,z)

where;

d₁ is the distance from the origin =

d₂ is the distance from (2,2,2) =

Also;

d₁ = 2d₂

By squaring both sides;

Collect the like terms:

Divide both sides by 3

Using the completing the square method;

∴

This is a sphere with a center    and ;

radius;

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign