Chapter 12, Problem 1RE

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8th Edition

James Stewart

ISBN: 9781305266643

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 *x*^{2} + *y*^{2} + *z*^{2} − 8*x* + 2*y* + 6*z* + 1 = 0

(a)

To determine

**To find:** An equation of the sphere that passes through the point

Explanation

Consider a sphere with center *r*.

**Formula used:**

Write the expression to find an equation of a sphere with center *r*.

Here,

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

**Calculation of the radius of the sphere** **:**

Substitute â€“1 for

(b)

To determine

**To find:** The curve in which the sphere intersects the

(c)

To determine

**To find:** The center and radius of the sphere.

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