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Chapter 14: Problem 61

Find an equation of the circle satisfying the given conditions. [ 13.1] Center \((0,0),\) radius 4

Short Answer

Expert verified
The equation is \( x^2 + y^2 = 16 \).

Step by step solution

01

Recall the Standard Form of a Circle's Equation

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

Substitute the Given Values

For a circle with center \(0,0\) and radius \(4\), substitute \(h = 0\), \(k = 0\), and \(r = 4\) into the standard form equation.
03

Write the Equation

After substituting the values, the equation becomes \( (x - 0)^2 + (y - 0)^2 = 4^2 \). Simplify to get \( x^2 + y^2 = 16 \).

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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
Understanding the standard form of a circle's equation is essential for solving any problem involving circles. The standard form is written as \( (x - h)^2 + (y - k)^2 = r^2 \). In this formula:

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