Chapter 10: Q 38 (page 789)

Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} - 2 x + 6 y - 8 z + 17 = 0$

Short Answer

Expert verified

The center is (1, -3, 4) and radius is 3.

Step by step solution

Given information

The given equation of a sphere is: $x^{2} + y^{2} + z^{2} - 2 x + 6 y - 8 z + 17 = 0$

Finding the radius and center

Converting the equation to whole square in variables $x, y and z :$

$x^{2} + y^{2} + z^{2} - 2 x + 1 + 6 y + 9 - 8 z + 16 + 17 - 26 = 0$

Isolating the variables:

${(x - 1)}^{2} + {(y + 3)}^{2} + {(z - 4)}^{2} = 3^{2}$

Comparing with equation of sphere, center is at (1, -3, 4) and radius is 3.

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Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} - 2 x + 6 y - 8 z + 17 = 0$

Short Answer

Step by step solution

Given information

Finding the radius and center

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Find the center and radius of the sphere with the given equation:x2+y2+z2-2x+6y-8z+17=0

Short Answer

Step by step solution

Given information

Finding the radius and center

One App. One Place for Learning.

Most popular questions from this chapter

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Statistics

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Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} - 2 x + 6 y - 8 z + 17 = 0$