   Chapter 12.1, Problem 24E

Chapter
Section
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 (5,4,9) .

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 and

r is the radius of a sphere.

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 (5,4,9) is |9| , which is 9. Thus, the distance from the center to the 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 (5,4,9) is |5| , which is 5. Thus, the distance from the center to the 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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