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Chapter 10: Problem 34

Find an equation of the circle satisfying the given conditions. Center \((0,0),\) radius 11

Short Answer

Expert verified
The equation of the circle is \[ x^2 + y^2 = 121 \]

Step by step solution

01

Identify the Circle's Standard Equation

The standard form of a circle's equation with center \( (h, k) \) and radius \( r \) is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \]
02

Substitute the Center Coordinates

Substitute the coordinates of the center, \( h = 0 \) and \( k = 0 \), into the standard form of the circle's equation: \[ (x - 0)^2 + (y - 0)^2 = r^2 \]
03

Simplify the Equation

Simplify the equation to get: \[ x^2 + y^2 = r^2 \]
04

Substitute the Radius

Substitute the given radius, \( r = 11 \), into the simplified equation: \[ x^2 + y^2 = 11^2 \]
05

Final Equation

Simplify the right side of the equation: \[ 11^2 = 121 \]. Thus, the equation of the circle is \[ x^2 + y^2 = 121 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Standard Form of a Circle
The standard form of a circle's equation is fundamental in geometry. It helps us understand the precise location and size of a circle on a coordinate plane. This form is expressed as:

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