   Chapter 12.1, Problem 16E

Chapter
Section
Textbook Problem

# Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

To determine

To find: An equation of the sphere that passes through the origin (0,0,0) and has the center (1,2,3).

Explanation

Formula used:

The expression to find an equation of a sphere with center C(h,k,l) and radius r is,

(xh)2+(yk)2+(zl)2=r2 (1)

Here,

(h,k,l) is the center of a sphere, which is (1,2,3) and

r is the radius of a sphere.

The expression to find the distance between two points P1(x1,y1,z1) and P2(x2,y2,z2).

|P1P2|=(x2x1)2+(y2y1)2+(z2z1)2 (2)

Calculation:

The radius of the sphere is the distance between the center of the sphere and the point through which the sphere passes.

In equation (2), substitute 1 for x1, 2 for y1, 3 for z1, 0 for x2, 0 for y2, and 0 for z2 to obtain the value of r as follows

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 