Distance Formula and Fixed Points Quiz

The equation of a sphere in 3D space is $x^2 + y^2 + z^2 = r^2$, where $(x, y, z)$ are the coordinates of any point on the sphere and $r$ is the radius of the sphere.

The formula for the distance $d$ between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in 3D space is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$.

The coordinates of the center of the sphere in the given text are $(0, 0, 0)$.

The radius of the sphere in the given text is $R$.

The general form of the equation of a sphere in 3D space is $x^2 + y^2 + z^2 + Ax + By + Cz + D = 0$, where $(x, y, z)$ are the coordinates of any point on the sphere and $A$, $B$, $C$, and $D$ are constants.