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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 11.10 (page 1076)

Write the standard form of the equation of the circle with a radius of $8$ and center $(0, 0)$ .

Short Answer

Expert verified

The required equation of the circle is $x^{2} + y^{2} = 64$ .

Step by step solution

01

Step 1. Concept Used

The standard form of the equation of a circle with center, $(h, k)$ , and radius, $r$ , is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

02

Step 2. Form the equation

The circle has a radius of $8$ and center $(0, 0)$ .

So use the standard form of the equation of a circle and substitute $0$ for $h$ , $0$ for $k$ , and $8$ for $r$ to form the equation as

$\begin{array}{rcl} {(x - h)}^{2} + {(y - k)}^{2} & = & r^{2} \\ {(x - 0)}^{2} + {(y - 0)}^{2} & = & 8^{2} \\ x^{2} + y^{2} & = & 64 \end{array}$

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