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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Equation of a Sphere In Exercises 29-38, find the standard equation of the sphere with the given characteristics. See Examples 4 and 5.

Center: (-4, 3, 6); tangent to the xy-plane

To determine

To calculate: The standard equation of sphere if the centre of sphere is (4,3,6) and tangent to the xy-plane.

Explanation

Given Information:

The centre of sphere is (4,3,6) and tangent to the xy-plane.

Formula used:

The standard equation of a sphere with centre at (h,k,j) and radius r is,

(xh)2+(yk)2+(zj)2=r2

Calculation:

The sphere has tangent to the xy-plane that means circumference of the sphere touches perpendicularly at a single point of xy-plane. The centre of the sphere is (4,3,6), which is six unit above the xy-plane.

The distance between the circumference of the sphere to centre of the sphere is known as radius of the sphere.

So, the radius of the sphere is 6 because the distance from xy-plane to centre of the sphere is 6 unit

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