Question

how to form an equation of a sphere ?

Answer 1

Equation of a sphere is very similar to that of a plane-disc(circular-region).
Consider Origin, O, of the $\text{R^{3}}$ space to be centre of the sphere of radius r.
Let point P(x,y,z) be a point inside or on the sphere.
Then, you'll have
$OP \leq r$
[tex] \sqrt{x^{2}+y^{2}+z^{2}} \leq r \\ \Rightarrow x^{2}+y^{2}+z^{2} \leq r^{2}[/tex].
More generally if C(u,v,w) is the centre $(x-u)^{2}+(y-v)^{2}+(z-w)^{2} \leq r^{2}$
Hence any second degree equation in three variables of sort 
$x^{2}+y^{2}+z^{2}+2ux+2vy+2wz+c \leq 0$ represents a sphere of centre C(-u,-v,-w) and radius, $r=\sqrt{u^{2}+v^{2}+z^{2}-c}$.

Answer 2

Answer:

Step-by-step explanation:

use distance formula