   Chapter 12, Problem 1RE

Chapter
Section
Textbook Problem

# (a) Find an equation of the sphere that passes through the point (6, −2, 3) and has center (−1, 2, 1).(b) Find the curve in which this sphere intersects the yz-plane.(c) Find the center and radius of the sphere x2 + y2 + z2 − 8x + 2y + 6z + 1 = 0

(a)

To determine

To find: An equation of the sphere that passes through the point (6,2,3) and has the center (1,2,1).

Explanation

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

Formula used:

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 (1,2,1) and

r is the radius of the sphere.

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

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

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

Calculation of the radius of the sphere (r):

Substitute –1 for x1, 2 for y1, 1 for z1, 6 for x2, –2 for y2, and 3 fo

(b)

To determine

To find: The curve in which the sphere intersects the yz-plane.

(c)

To determine

To find: The center and radius of the sphere.

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