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Chapter 10: Q 8 (page 848)

Given a sphere with center (4, 6, 2), (1, 3, -5) is a point on the sphere.

Short Answer

Expert verified

The required equation is:

${(x - 4)}^{2} + {(y - 6)}^{2} + {(z - 2)}^{2} = 62$

Step by step solution

01

Given information

Given a sphere with center (4, 6, 2), (1, 3, -5) is a point on the sphere.

02

Finding the radius of sphere

The radius of sphere will be the distance between the center and given point on sphere.

Radius, using the distance formula, is:

$\sqrt{{(1 - 3)}^{2} + {(3 - 6)}^{2} + {(- 5 - 2)}^{2}}$

Radius is:

$\sqrt{62}$

03

Finding the equation

The required equation is:

${(x - 4)}^{2} + {(y - 6)}^{2} + {(z - 2)}^{2} = {(\sqrt{62})}^{2}$

Simplify:

${(x - 4)}^{2} + {(y - 6)}^{2} + {(z - 2)}^{2} = 62$

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Most popular questions from this chapter

Use the Intermediate Value Theorem to prove that every cubic function $f (x) = A x^{3} + B x^{2} + C x + D$ has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

Find a unit vector in the direction opposite to $<3, 4, 5>$ .

Find $u + v a n d u - v$ also sketch $u, v, u + v, u - v$

role="math" localid="1649603034674" $u = (1, - 4, 6) a n d v = (2, - 4, 7)$

Find a vector of length 3 that points in the direction opposite to $<1, - 2, 3>$ .

In Exercises 30–35 compute the indicated quantities when $u = (- 3, 1, - 4), v = (2, 0, 5), and w = (1, 3, 13)$

$u \times w and w \times u$

See all solutions

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