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 reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

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step-by-step explanation: