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Chapter 9: Q. 70 (page 622)

In Problems 69 and 70, find the equation of a sphere with radius r and center $P_{0}$ .
$r = 2; P_{0} = (1, 2, 2)$

Short Answer

Expert verified

The equation of sphere is

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

Step by step solution

01

Step 1. Given

Given radius as well as center of the sphere as:

$r = 2; P_{0} = (1, 2, 2)$

02

Step 2. Calculation

By applying the standard equation of sphere we get:

$r^{2} = {(x - x_{0})}^{2} + {(y - y_{0})}^{2} + {(z - z_{0})}^{2}$

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

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Most popular questions from this chapter

Rose curves are characterized by equations of the form $r = a \cos (n θ) o r r = a \sin (n θ), a \neq 0 .$ If $n \neq 0$ is even, the rose has _____ petals; if $n \neq \pm 1$ is odd, the rose has ______ petals.

Write the expression in the standard form $a + b i$ .

${[\sqrt{3} (\cos 10 ° + i \sin 80 °)]}^{3}$

Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 2 + 4 \cos θ$

In Problem, the vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 4 + 2 \sin θ$

See all solutions

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