   Chapter 12.1, Problem 13E

Chapter
Section
Textbook Problem

# Find an equation of the sphere with center (−3, 2, 5) and radius 4. What is the intersection of this sphere with the yz-plane?

To determine

To find: An equation of the sphere with center (3,2,5) and radius 4 and the intersection of the sphere with the yz-plane.

Explanation

Consider a sphere with center C(h,k,l) and radius r.

Formula:

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

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

Here,

(h,k,l) is the center of a sphere, which is (3,2,5) and

r is the radius of a sphere, which is 4.

Calculation:

In equation (1), substitute 3 for h , 2 for k , 5 for l , and 4 for r .

[x(3)]2+(y2)2+(z5)2=42(x+3)2+(y2)2+(z5)2=16

Thus, the equation of the sphere with center (3,2,5) and radius 4 is, (x+3)2+(y2)2+(z5)2=16_

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