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Chapter 10: Q. 6 (page 848)

Find the equation of the sphere center at \((2,-3,4)\) and tangent to the \(xz\) plane.

Short Answer

Expert verified

The equation of sphere is \(x^2+y^2+z^2-4x+6y-8z+20=0\).

Step by step solution

01

Given Information

The center at \((2,-3,4)\).

The tangent plane to the sphere is (\xz\) plane.

02

Find the radius

Since \(xz\) plane is tangent of the sphere, the radius is the y-coordinate of the center.

Therefore, the radius is \(r=3\).

03

Find the equation of sphere

Substitute \((2,-3,4)\) and \(r=3\) into equation of sphere.

\((x-2)^2+(y+3)^2+(z-4)^2=3^2\).

Simplify the equation and the equation is,

\(x^2+y^2+z^2-4x+6y-8z+20=0\).

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Most popular questions from this chapter

In Exercises 22–29 compute the indicated quantities when u=(2,1,−3),v=(4,0,1),andw=(−2,6,5)

Find the area of the parallelogram determined by the vectors u and v.

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Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

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