Question

(x-4)2+(y+3)2+(z+4)2=4

Answer 1

2х-8+2y+6+2z+8=4
2x+2y+6+2x=4
2x=4-2y-6-2z
2x=-2-2y-2z
x=-1-y-z
y€R, z€R

Answer 2

The equation you've provided is the equation of a sphere in 3D space. It represents a sphere centered at the point (4, -3, -4) with a radius of 2.

The general form of the equation of a sphere in 3D space is:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

Where:

• (h, k, l) are the coordinates of the sphere's center.
• r is the radius of the sphere.

In your equation, you have (x-4)^2 + (y+3)^2 + (z+4)^2 = 4, which matches the general form with (h, k, l) = (4, -3, -4) and r^2 = 4, so the radius, r, is 2.

This equation describes all the points in 3D space that are a distance of 2 units from the point (4, -3, -4), forming a sphere with that center and radius.