Chapter 10: Q 39 (page 789)

Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} + 3 y - 5 z + 3 = 0$

Short Answer

Expert verified

The center is $(0, \frac{- 3}{2}, \frac{5}{2})$ and radius is $\frac{\sqrt{22}}{2}$

Step by step solution

Given information

A sphere with the equation $x^{2} + y^{2} + z^{2} + 3 y - 5 z + 3 = 0$

Finding the center and radius

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

$x^{2} + y^{2} + z^{2} + 2 \times \frac{3}{2} y - 2 \times \frac{5}{2} \times z + {(\frac{3}{2})}^{2} - {(\frac{3}{2})}^{2} + {(\frac{5}{2})}^{2} - {(\frac{5}{2})}^{2} + 3 = 0$

Segregating the terms:

$x^{2} + {(y + \frac{3}{2})}^{2} + {(z - \frac{5}{2})}^{2} = {(\frac{\sqrt{22}}{2})}^{2}$

Comparing with equation of a sphere, the center is $(0, \frac{- 3}{2}, \frac{5}{2})$ and radius is $\frac{\sqrt{22}}{2}$ .

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Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} + 3 y - 5 z + 3 = 0$

Short Answer

Step by step solution

Given information

Finding the center and radius

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Find the center and radius of the sphere with the given equation:x2+y2+z2+3y-5z+3=0

Short Answer

Step by step solution

Given information

Finding the center and radius

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Find the center and radius of the sphere with the given equation:
$x^{2} + y^{2} + z^{2} + 3 y - 5 z + 3 = 0$