Chapter 12.1, Problem 24E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant.

To determine

**To find:** An equation of the largest sphere when it is contained in the first octant with center

Explanation

Consider a sphere with center
*r*.

**Formula:**

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

Here,

The radius of the largest sphere that contained in the first octant is the minimum distance from the center to the any of the three coordinate planes.

The distance from any point to the *xy*-plane is the absolute value of *z*-coordinate of the point.

The absolute value of *z*-coordinate of the point
*xy*-plane is 9.

The distance from any point to the *yz*-plane is the absolute value of *x*-coordinate of the point.

The absolute value of *x*-coordinate of the point
*yz*-plane is 5.

The distance from any point to the *xz*-plane is the absolute value of *y*-coordinate of the point

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