Chapter 9, Problem 12RCC

To determine

To find: The equation of the sphere.

Answer to Problem 12RCC

The equation of the sphere. is ${\left(x-a\right)}^2+{\left(y-b\right)}^2+{\left(z-c\right)}^2=r^2$ .

Explanation of Solution

Given Information:

The centre of the sphere is at $\left(a,b,c\right)$ and the radius is $r$ .

Concept used:

A three-dimensional coordinate system can be formed by passing a z -axis perpendicular to both the x -axis and the y -axis at the origin.

The standard form of the equation of the sphere is given as,

${\left(x-h\right)}^2+{\left(y-k\right)}^2+{\left(z-j\right)}^2=r^2$

The standard form of the equation of the sphere is written as,

$\begin{array}{l}{\left(x-h\right)}^2+{\left(y-k\right)}^2+{\left(z-j\right)}^2=r^2\\ {\left(x-a\right)}^2+{\left(y-b\right)}^2+{\left(z-c\right)}^2=r^2\end{array}$

Thus, the equation of the sphere. is ${\left(x-a\right)}^2+{\left(y-b\right)}^2+{\left(z-c\right)}^2=r^2$ .