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

Step 1. Concept Used

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

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

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Form the equation

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

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Form the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Applied Mathematics

Decision Maths

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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